Question

Hello! How would you solve Log_5(2x)=log_5(2^3)-log_5(12)?

Answer 1

First you'll use log rule #2 described on this page

http://www.purplemath.com/modules/logrules.htm

Answer 2

That will turn

\[\Large \log_{5}(2x) = \log_{5}(2^3) - \log_{5}(12)\]

into

\[\Large \log_{5}(2x) = \log_{5}\left(\frac{2^3}{12}\right)\]

Answer 3

agreed so far?

Answer 4

Yes.

Answer 5

we have logs of the same base on either side of the equal sign

so the stuff inside the logs must be equal

\[\Large \log_{5}(2x) = \log_{5}\left(\frac{2^3}{12}\right)\]

\[\Large 2x = \frac{2^3}{12}\]

solve for x

Answer 6

well thats the thing. My answer key provided by my teacher said that x was 1/3 but i keep getting 3

Answer 7

oh wait! I got 1/3. Thank you so much!

Answer 8

glad to be of help