Question

logarithmic equation? log2 (x+2) - log2 (x-5) =3

Answer 1

\[\log_2 (x+2) - \log_2 (x-5) = \log_2 2^3\]

Answer 2

Can you solve further?

Answer 3

start with
\[\log_2(\frac{x+2}{x-5})=3\] the rewrite in equivalent exponential form

Answer 4

first equality because
\[\log(A)-\log(B)=\log(\frac{A}{B})\]

Answer 5

then go to
\[\frac{x+2}{x-5}=2^3=8\] and then algebra from there on in