Question

I'm reposting this problem because I couldn't understand how x=16/7 could someone do this step by step so I'm able to understand? Thank you

log(base 2)x-log(base 2)(x-2)=3

Answer 1

\[\log_2(x)-\log_2(x-2)=3\] step one is to write as a single logarithm, you do this as
\[\log_2(\frac{x}{x-2})=3\] is that ok?

Answer 2

combine the logs so that u have log(base 2) (x/x-2) = 3 using log rules

then u raise both sides with a base 2 to get rid of the logs:

x/(x-2) = 2^3

x = 8(x-2)

x=16/7

Answer 3

because that is the main step. then rewrite in equivalent exponential form and get
\[\frac{x}{x-2}=2^3\] and go from there to solve for x

Answer 4

what qed said