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

Question

jim_thompson5910 · Answer

First you'll use log rule #2 described on this page http://www.purplemath.com/modules/logrules.htm

jim_thompson5910 · Answer

That will turn

$$\Large \log_{5}(2x) = \log_{5}(2^3) - \log_{5}(12)$$

into

$$\Large \log_{5}(2x) = \log_{5}\left(\frac{2^3}{12}\right)$$

jim_thompson5910 · Answer

agreed so far?

anonymous · Answer

Yes.

jim_thompson5910 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

glad to be of help