Question

Which of the following is the solution of log ( base x – 3) 0.001 = –3 ?


x = 15

x = 5

x = 7

x = 13 Which of the following is the solution of log ( base x – 3) 0.001 = –3 ?


x = 15

x = 5

x = 7

x = 13 @Mathematics

Answer 1

\[\log_{x-3}(.001)=-3 \]
First exponentiation both sides to remove the "log"
\[.001=(x-3)^{-3}\]
invert both sides to get rid of the negative exponent
\[1/.001=1000=(x-3)^{3}\]
take the cube root of both sides
\[10=x-3\]