Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
I need to solve for x: log(base 5x + 9) (x^2 + 6x + 9) + log(base x+3) (5x^2 + 24x + 27) = 4
 one year ago
 one year ago
I need to solve for x: log(base 5x + 9) (x^2 + 6x + 9) + log(base x+3) (5x^2 + 24x + 27) = 4
 one year ago
 one year ago

This Question is Closed

Dido525Best ResponseYou've already chosen the best response.1
\[\log_{5x+9} (x^2+6x+9)+\log_{x+3} (5x^2+24x+27) = 4\] Is that the question?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
They don't have the same base?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Darn... This complicates things...
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
\[\log_{5x+9}(x+3)^{2}+\log_{x+3} ((5x+9)(x+3))\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Can you see anyway to simplify this? :) .
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
You have two logs multiplied. What can you do? :) .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
This is a type of a bonus, so we never learned this (I thought of factoring but idk how to xD). Is it possible to get both logs to the same base? By putting them both to the power of (5x+9)(x+3)
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
They don't have the same base so you can't do "loga + logb = log(a*b)"
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I meant for the right log :) .
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Ohh you need help factoring? Okay: dw:1351987084250:dw
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
You do log (5x^2 + 24x + 27)/(x+3)
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Wait I am still in the process of solving this :P .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
and do that for both, lol okay. I'll try solving it here like that
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Wow this is the hardest log I have done so far :P .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah, same. Never seen anything like it. But I think it'll work out nicely
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@Dido525 your approach is correct. think of making use of the change of base for logs you'll be there.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
That was my next plan :P .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@lucenzo do you know about the change of base formula for logs?
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
no. I think I might have to solve this question w/o using the formula, since we never learned it
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
I can't see how to solve this without using that formula?
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
okay, nvm then. Can you tell me what the formula is?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But you have too O_o .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
I would assume that if this is a /bonus/ question, then the teacher expected some of you to do some learning on your own to try and solve this.
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
converting bases isn't advanced... iirc.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
change of base is given by:\[\log_ax=\frac{\log_bx}{\log_ba}\]
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
you usually learn it first...
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
that is what thought @Algebraic!
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
Oh, I've used that formula LOL. I actually was thinking that from the beginning. In this case I did \[\log_{a}n \] first
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Well actually you don't have to use change of base :) .
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Wait. Hold yon. You might :P .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
then I faactored both trinomials and it was log(base 10) so I was able to multiply the logs and now I've ended up w/ a strange trinomial: \[x^{2} + 6x  9991 = 0\]
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
did you get that? @Dido525
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
I got x =3/2, 1 haven't checked it however...
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
did you get this trinomial tho: x^2+6x−9991=0
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
No you don't get that...
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
I think I did it wrong
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
@Algebraic! I got only 3/2 .
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
\[\log_{5x+9}(x+3)^{2}+\log_{x+3} ((5x+9)(x+3)) \] We were at that step.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Use the properties of logs to expand that right log: @lucenzo
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
I think you have a typo there @Dido525  they should all be base (x+3)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
\[\log_{x+3} ((5x+9)(x+3))=\log_{x+3} (5x+9)+\log_{x+3} (x+3)\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
\[\log_{x+3} ((5x+9)(x+3))=\log_{x+3} (5x+9)+\log_{x+3} (x+3)=4\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Are you there? @lucenzo
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah. So we can expand all of the logs right?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@Dido525 your last equation is wrong  you have forgotten the other log term
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I am ignoring that one for now :P .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
then it shouldn't be set "= 4"
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
it would be 3 then? Instead of 4
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So expanding all that you should get: \[\log_{5x+9}(x+3)^{2}+\log_{x+3} (5x+9)+\log_{x+3} (x+3)=4\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Do you notice anything special about the last log term? @lucenzo
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah, its the same thing over the same thing. So it is 1. You move that to the other side and the "4" becomes a "3"
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So you should get : \[\log_{5x+9}(x+3)^{2}+\log_{x+3} (5x+9) =3\]
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
I got to that part no problem. The next part is what confuses me xD
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Now what do you notice about the first log term?
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
\[\log_{5x+9} (x+3)^2 = \frac{ 2}{\log_{x+3} (5x+9) }\] \[\log_{x+3} (5x+9)(x+3) = 1 +\log_{x+3} (5x+9)\] \[\log_{x+3} (5x+9)+\frac{ 2}{\log_{x+3} (5x+9) }=3\]
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah, I expanded the first term
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Remember, in a log you can bring that power down :) .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
powering every term in the equation by the same number?
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
quadratic in \[\log_{x+3} (5x+9) \]
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
I see now xD thanks you
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So you should get : \[2\log_{5x+9}(x+3)+\log_{x+3} (5x+9) =3\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Now use change of base that you learned a little earlier. :) .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
I know the normal way of using that rule where it would be: \[\log(x+3)/\log(5x+9) \]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Hint: Use it on the right log :) .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
are we assuming that the "y" is just 10. so its log base of 10?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Ahh but in this case that rule is useless. Besides you can't use that unless they have the same base.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Well in this case it's base x+3 .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
no, i meant for the first term. the term on the left
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
just for the \[\log_{5x+9}(x+3) \]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
The base is 5x+9 for that yes.
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah, that's why i did \[\log(x+3)/\log(5x+9)\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
The trick for the right log is that you want to convert that right base to the base on the left log.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
That's correct but you want base 5x+3 .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
I got 1/\[1/\log_{5x+9}(x+3) \]
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
whoops, just meant to put 1 "1/"
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
and now we put everything to the power of *5x+9* ?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So you should now have: \[2\log_{5x+9}(x+3)+1 =3\log_{5x+9} (x+3)\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Move the common terms to one side.
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah lol, I was about to say that
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@Dido525  are you sure of your last step?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
remember you started from:\[2\log_{5x+9}(x+3)+\frac{1}{\log_{5x+9} (x+3)} =3\]
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
can we not put it all to ther power of 5x+9 tho? I'm still thinking it might be simpler
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
from this point, it might be better to do what @Algebraic! did, i.e. let:\[u=log_{5x+9}(x+3)\]to get:\[2u+\frac{1}{u}=3\]and then solve this quadratic in u first.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
do you understand this step @lucenzo ?
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
Yeah, I'm gonna try it
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I only get one solution >.> .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
we got to:\[2u+\frac{1}{u}=3\]multiply both sides by u to get:\[2u^2+1=3u\]\[2u^23u+1=0\]this should have 2 solutions for u. then use the fact that:\[u=log_{5x+9}(x+3)\]to find all the x values.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I only get 1 answer :( .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
there are 3 answers altogether  @lucenzo have you solved the quadratic in u yet?
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah I got u = 1 or 1/2
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
what would be the third answer?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
that is correct. so now you need to solve:\[log_{5x+9}(x+3)=1\]and:\[log_{5x+9}(x+3)=0.5\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
so, starting with:\[log_{5x+9}(x+3)=1\]what do you get for x?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Now I got it at last :D .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
remember that if:\[\log_ba=c\]then:\[a=b^c\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
are you stuck @lucenzo ?
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah, but I just realized I had a 2 multiplied to the log term (I'm gonna try it without the 2)
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
I got 3/2 for the first one (if x = 1)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
plz double check your work  I think you have made an error in the "sign" of the result. and it is for (u=1) not (x=1)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
it might be better if you showed your steps here so that we can help you spot where you may have made a mistake
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
I took the equation you had then I put both sides to the power of 5x+9 like so:
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
not quite right @Dido525
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
The 1 is incorrect right?
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
\[5x+9^{\log_{5x+9}(x+3) } = 5x+9^1\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@lucenzo you are over complicating this.
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
that's right, actually.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
yes  that is correct  but you could have got there in one step. remember:\[\log_ba=c\implies a=b^c\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
yeah it's correct but why would you do that? :( .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
That's the way we learned to write it
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
Just a way of showing how to get there, it's just the same thing
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
ok  fair enough  if that is how you were taught then you should stick to that method.
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
I think I just showed the work
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Yeah it's correct regardless.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
ok so what x value do you get from this?
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
6/4 which reduces to 3/2
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I keep getting  3/2 hmm...
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
this step was correct:\[x5x=93\]which then leads to:\[4x=6\]
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
uhoh, I made a sign error xD. I wrote 6
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
you're right. It's 3/2
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
ok, so first solution is x=1.5. next, you need to solve this for x:\[log_{5x+9}(x+3)=0.5\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
again here it would help if you listed your steps
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
@asnaseer : I got so far: dw:1351991548862:dw
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
\[x+3=(5x+9)^{\frac{ 1 }{ 2 }}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@Dido525 where did you derive that first equation from? @lucenzo that is correct  now square both sides
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
You get 0 and 1 if you solve for x.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
If you solve x I keep getting 0 and 1.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
This thread is so epic I am lagging >.< .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
@Dido525 please let @lucenzo solve this
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
now factorise and solve
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Sorry about that anaseer.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I am kinda into the problem XD .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
I know some problems are so intriguing that we feel compelled to try and solve them ourselves  it is only natural. :)
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
i did the quadratic formula and got x = 1 or 0
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
you have the right answer
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
but you did not need to use the quadratic formula
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Yeah I got that too :) . I just had a silly algebra error.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
You could have factored :P .
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
\[x^2+x=0\]\[x(x+1)=0\]so\[x=0\]or:\[x=1\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
so final solution is: x = 1.5 or 1 or 0
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
yeah, and I think ALL of them work. so none are extraneous
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Yeah. I checked. All work.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
correct  and thanks for posting such an interesting problem @lucenzo :)
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I agree! I am in uni and this was the toughest log I have done in ages :) .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
lol. I'm the one to thank you guys. Thank you sooo much! You all really helped my very much. I'm in high school right now, and when I take calculus next semester and have to do a log question like this, I'll feel like I'm ahead of the others xD
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
yw :) and keep up the hunger for knowledge my friend! :)
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Calculus is very fun! You will enjoy it a lot :) .
 one year ago

lucenzoBest ResponseYou've already chosen the best response.0
Thanks, I heard that it has less writing and that you learn 'tricks' for solving questions ALOT quicker (like never before)
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.