find x, given 1/3 log 81^(x) = -1/4

Question

zpupster · Answer

mult by 3 both sides gives

log81^x = -3/4  eliminate the log
81^x= e^-3/4  tnhen talke log base 81 bothsides
leaves us with

x=-3/4log(81)

alekos · Answer

thats not quite right , but nice try

anonymous · Answer

First off, multiply both sides by a constant to simplify the equation. In this equation, we will multiply both sides by 3.

log^x(81)=-3/4 is what you are left with.

Eliminate the exponential from the left hand side. Take the logarithm base log(81) of both sides:

$$x=\frac{ i \pi (2n+1) }{ \log(\log81)) } - \frac{ \log (\frac{ 4 }{ 3 }) }{ \log(\log81)) } for n \in z$$

anonymous · Answer

Erm, guess the system for the equation showing is not working? ._.

alekos · Answer

not sure how you got this? doesnt look right either

alekos · Answer

z pupster 

is it log to the base 10 of 81 to the power of x?

anonymous · Answer

Anyhow........

Hold on, I'm going to show images that I have made in Microsoft word, second. Let me type the work and my final answer.

alekos · Answer

wait for zpupsters reply

alekos · Answer

sorry i meant gmk 

is it log to the base 10 of 81 to the power of x?

alekos · Answer

gmt, are you there?

anonymous · Answer

Here are the images, labeled with "Step 1, Step 2, etc".

anonymous · Answer

Gah, school computer renamed the files when I uploaded... but there ya go..

alekos · Answer

gmt's gone