Question

log x- log (x-2)= 4
both logs have a base of 2
find x, show steps

Answer 1

the answer is 32/15 but i keep getting no solution

Answer 2

\[\log_2\left(\frac{x}{x-2}\right)=4\] is how you want to begin

Answer 3

\(\large\color{teal}{ \log_2x-\log_2(x-2)=4 }\)

\(\large\color{teal}{ \log_2x=4+\log_2(x-2) }\)

\(\large\color{teal}{ \log_2x=4\times \log_22+\log_2(x-2) }\)

\(\large\color{teal}{ \log_2x= \log_22^4+\log_2(x-2) }\) continue....

Answer 4

then write is in equivalent exponential form

Answer 5

\[\frac{x}{x-2}=2^4\] is the exponential form

Answer 6

or better yet
\[\frac{x}{x-2}=16\]

Answer 7

solve that for \(x\)

Answer 8

you good with that ? that is how you are going to get the \(\frac{32}{15}\) that you know is the answer

Answer 9

yeah, thanks