Question

Which of the following is the solution of log (x – 5) 0.001 = –3
a.) x=5
b.) x=7
c.) x=13
d.) x=15

Answer 1

\[\log_{x-5}{0.001}=-3\]\[\implies (x-5)^{-3}=0.001.\]\[\implies (x-5)^{-3}=\frac{1}{1000}=\frac{1}{10^3}=10^{-3}.\]\[\implies (x-5)^{-3}=10^{-3} \implies (x-5)=10 \implies \color{blue}{x=15.}\]

Answer 2

Remember;

\[\huge{\color{red}{\log_a{b}=x.}}\]\[\huge{\color{red}{\implies a^x=b.}}\]