Question

alright mates, gonna need some help on this what is the solution of the equation 9^(2x)=6?
round answer to the nearest ten thousandth

Answer 1

take the log (base 10 is ok) of both sides
\[ \log_{10}\left(9^{2x}\right) = \log_{10}(6) \]
use the property
\[ \log(a^b) = b \log(a) \]
to "get at" the 2x

you will need a calculator to find a value for x.

Answer 2

alriiiiight haha, seeing as how i don't have a calculator is there another way to do this?

Answer 3

you can type the problem into google.

but first you have to solve for x.
can you do that ?

Answer 4

nope :P i did attempt several times before posting my question but i cant math :P

Answer 5

match up this
\[ \log(a^b) = b \log(a) \]
with the left side of your problem
\[ \log\left(9^{2x}\right) = \log(6) \]

the idea is to rewrite the left side, using that rule

Answer 6

alright thanks :)

Answer 7

can you rewrite the left side, using that rule ?

Answer 8

i can try xD

Answer 9

Look at it this way. We're 'shifting' the \(2x\) to the front.