UnknownRandom
  • UnknownRandom
Could somebody help me with this log problem?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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cutiecomittee123
  • cutiecomittee123
what is it
UnknownRandom
  • UnknownRandom
4log4(3)-log4(4)
UnknownRandom
  • UnknownRandom
The answer can't contain a log

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More answers

cutiecomittee123
  • cutiecomittee123
I am really rusty and logs because I havent done them in a year or so. But I think you have to convert it to a diferent form inorder to solve it
Nnesha
  • Nnesha
familiar with the log properties ?
UnknownRandom
  • UnknownRandom
Yep.
Nnesha
  • Nnesha
alright apply log property start with the power rule
UnknownRandom
  • UnknownRandom
log4(81/4)?
Nnesha
  • Nnesha
looks good
Nnesha
  • Nnesha
now set it equal to x or use change of base formula
Nnesha
  • Nnesha
if we set it equal to x we should change log to exponential form
UnknownRandom
  • UnknownRandom
I can't remember how to do that.
Nnesha
  • Nnesha
for change of base formula \[\huge\rm log_b a = \frac{ \log a }{ \log b }\]
Nnesha
  • Nnesha
and if you want to do it by hands so set it equal to x |dw:1443129484346:dw|
UnknownRandom
  • UnknownRandom
|dw:1443129612389:dw|
UnknownRandom
  • UnknownRandom
Is that right?
UnknownRandom
  • UnknownRandom
Solving for that power?
Nnesha
  • Nnesha
yes let missing exponent equal to x and then write 81 in terms of base 4
Nnesha
  • Nnesha
4 to the what power =81?
UnknownRandom
  • UnknownRandom
Wait, why can you cancel that 4?
UnknownRandom
  • UnknownRandom
in 81/4
Nnesha
  • Nnesha
how would you cancel it ?
UnknownRandom
  • UnknownRandom
How did you get rid of that 4 in 81/4?
Nnesha
  • Nnesha
we should rewrite 81 in terms of base 4 so we can apply the exponent rule \[\huge\rm \frac{ x^m }{ x^n }=x^{m-n}\]
Nnesha
  • Nnesha
we need 4 base at the numerator so rewrite 81 in terms of base 4 4 to the what power = 81 ?
Nnesha
  • Nnesha
alright wait a sec
Nnesha
  • Nnesha
ahh i see we can't write 81 in terms of base 4 3^4 = 81 i was thinking 4^3 sorry about that
Nnesha
  • Nnesha
well u have to take log to solve for x so jsut use change of base formula that would be easy
UnknownRandom
  • UnknownRandom
I was lost. The application we use to answer questions won't take answers with log in it. So what do you recommend?
Nnesha
  • Nnesha
change of base formula
UnknownRandom
  • UnknownRandom
How do write that?
UnknownRandom
  • UnknownRandom
*you
Nnesha
  • Nnesha
\[\huge\rm \log_\color{blue}{b} \color{ReD}{a} =\frac{ \log\color{red}{ a} }{ \log \color{blue}{b} }\]
UnknownRandom
  • UnknownRandom
log (81/4)/log(4)?
Nnesha
  • Nnesha
good right!!
UnknownRandom
  • UnknownRandom
Do you subtract the two now?
Nnesha
  • Nnesha
subtract no just divide them we don't need the original question
UnknownRandom
  • UnknownRandom
True, but on our test we can't use calculators so I don't know how I would do that division without one.
Nnesha
  • Nnesha
can't use calculator hm i mean not just for log(4) ???
UnknownRandom
  • UnknownRandom
Nope, but we will probably be able to use log in our answers on the test.
Nnesha
  • Nnesha
we have to use calculator for this one bec 81/ 4 is a decimal answer u were asking can we multiply 4 both sides ? yes you can |dw:1443130983953:dw|
Nnesha
  • Nnesha
when we multiply same bases we should `add` exponents \[\huge\rm x^m \times x^n=x^{m+n}\] \[\large\rm 4^1 \times 4^x =81 ~~~~~~~~~~4^{1+x}=81\]
UnknownRandom
  • UnknownRandom
So how do you find x?
Nnesha
  • Nnesha
now take log both sides to move the exponent at front \[ \huge\rm (1+x )\log(4) = \log (81)\] now u can solve for x
Nnesha
  • Nnesha
divide both sides by log(4) and then subtract 1
UnknownRandom
  • UnknownRandom
Ok, I got 2.169925001 but it said the answer was wrong.
Nnesha
  • Nnesha
http://www.wolframalpha.com/input/?i=4log4%283%29-log4%284%29 that's the correct answer
Nnesha
  • Nnesha
is there any statement round some hundred/thousandth ?
UnknownRandom
  • UnknownRandom
Nope
Nnesha
  • Nnesha
well i round it hundred place 2.169925001 (two numbers after decimal if the the 3rd is 5 or greater than 5 then we can wround to 7) 2.169925001 hundredths place 2.17
Nnesha
  • Nnesha
did they gave u the right answer ?
UnknownRandom
  • UnknownRandom
Nope :(
Nnesha
  • Nnesha
ugh that's what i got and that's exactly what on this calc http://www.wolframalpha.com/input/?i=4log4%283%29-log4%284%29
UnknownRandom
  • UnknownRandom
I don't know then. Thanks for the help though.
Nnesha
  • Nnesha
alright ask ur teacher let me know what 's the correct answer if that's not right good luck!
UnknownRandom
  • UnknownRandom
I just typed 3/4 and it worked. Wow.... I guess the 4 wasn't supposed to be there on that problem. @Nnesha
Nnesha
  • Nnesha
3/4 ? what 4 wasn't supposed to be there ?
UnknownRandom
  • UnknownRandom
I guess not. Somebody done messed up.
UnknownRandom
  • UnknownRandom
and wasted 2 hours of my life.
Nnesha
  • Nnesha
i don't get it so what was the question ?
UnknownRandom
  • UnknownRandom
The question was evaluate 4*log4(3)-log4(4)
Nnesha
  • Nnesha
so 4 isn't a base ?
Nnesha
  • Nnesha
\[4 \log4(3) - \log4(4)\] like this or \[4\log_4 (3) - \log_4(4)\]
UnknownRandom
  • UnknownRandom
The second one
Nnesha
  • Nnesha
okay there is 4 at front of log so we have to apply the power rule right
UnknownRandom
  • UnknownRandom
Yep
Nnesha
  • Nnesha
so \[\log_4 (3)^4 - \log_4 4 = \log_4 \frac{ (3)^4 }{ 4 }\] that's what we did so what was the mistake ? o.O hmm
UnknownRandom
  • UnknownRandom
I think it was typed wrong and the 4 in the front shouldn't have been there.
Nnesha
  • Nnesha
oh okay so \[\large\rm \log_4 \frac{ 3 }{ 4 }\]
UnknownRandom
  • UnknownRandom
That's what I think.
Nnesha
  • Nnesha
that will give u the negative answer
Nnesha
  • Nnesha
we can just guess if we don't know what the question is exly
UnknownRandom
  • UnknownRandom
\[4\log_4{3}-1 \]
UnknownRandom
  • UnknownRandom
So \[\frac{ \log3 }{ \log4 }-1\]
UnknownRandom
  • UnknownRandom
= -.208
UnknownRandom
  • UnknownRandom
4^-.208 = 3/4
UnknownRandom
  • UnknownRandom
@Nnesha
UnknownRandom
  • UnknownRandom
4^log4(3)-log4(4) That is what the problem was supposed to say.
Nnesha
  • Nnesha
take a screenshot plz you're not sure abt the question ..

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