A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Have a few problems I was stuck on.
1)log_9(x+4)+log_9(x4)=1
2)Sqrt(3x2)sqrt(x)=1
 2 years ago
Have a few problems I was stuck on. 1)log_9(x+4)+log_9(x4)=1 2)Sqrt(3x2)sqrt(x)=1

This Question is Closed

GregTheo
 2 years ago
Best ResponseYou've already chosen the best response.0First combine the logs ( addition of log is multiplication) log(x+4) + log(x4) = Log ((x+4)/(x4)) raise everything from base 9 for part one, doing this cancels the log because they are inverse functions and 9^1 is just 9 resulting in (x+4)(x4) = 9 distribute x^2 16 = 9 x^2 = 25 x= + or 5

GregTheo
 2 years ago
Best ResponseYou've already chosen the best response.0typo, the log product should read log ((X+4)(x4))

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1ok lets solve it since \[\Large \log(a)+\log(b)=\log(ab)\] (addition changes to multiplication \[\Large \log _{9}((x+4)(x4))=1\] since \[\Large a^2b^2=(a+b)(ab)\] so \[\Large \log _{9}(x^216)=1\]

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, I got as far as @sami21 But got stuck. I knew the answer was 5. Didnt know how to get it.

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1so now we can cgange the log by change of bass formula

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm..thats where i got stuck. How do you do that?

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1\[\Large \log _{a}(b)=\frac{\ln(a)}{\ln{b}}\]

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1it is upto use to change it to any base .i used natural log whose base is e

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm...i think i get it.

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0I had another one similar to it: 7^(5x2)=5^(3x)

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0I know you have to log both sides.

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1yes take ln of both sides

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1then use property \[\Large \log _{a}(b)^n=nlog _{a}b\] which means exponents gets down and gets multiplied !

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1let me do the your question now using above property

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1take ln of both sides\[\Large \ln(7)^{5x2}=\ln(5)^{3x}\] so using the above mentioned property \[\Large (5x2)\ln(7)=(3x)\ln(5)\]

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1now use calculator to find values of ln7 and ln5

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1ln(7)=1.94 ln(5)=1.60 (5x2)*(1.69)=(3x)1.609

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0Yesss. I can take it from there, thank you so much! And the last one, so sorry, is b on the question.

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1a typo ! correct is (5x2)*(1.94)=(3x)1.609

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1ok. u mean this \[\Large \sqrt{3x2}\sqrt{x}=1\] ??

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1ok taking square of both sides

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1we have \[\Large (\sqrt{3x2}\sqrt{x})^2=1^2\] using \[\Large (ab)^2=a^2+b^22ab\] we have \[\Large ((3x2)+x2\sqrt{3x2}\sqrt{x})=1\]

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0Itsokay i will pretend the 2 was really 3

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1its ok :) i am notorious for typo mistakes ask anyone here :P

sami21
 2 years ago
Best ResponseYou've already chosen the best response.1have a look at here http://www.wolframalpha.com/input/?i=solve%28sqrt%283x3%29sqrt%28x%29%3D1%29 its quite difficult to type :P

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0Wow, thats good enough! Thank you soo much for your help. I learned a lot!

GOODMAN
 2 years ago
Best ResponseYou've already chosen the best response.0Also, thank you too @GregTheo

muhammad9t5
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt(3x2)\sqrt(x)=1\] add \[\sqrt(x)\] in both sides
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
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.