Write the expression using only the indicated logarithms.
-$\log _ { 1 / 6 } ( a - b )$ using common logarithms
A) $\frac { \log ( a - b ) } { \log 6 }$
B) $\frac { 1 } { \log 6 }$
C) $- \frac { \log ( a - b ) } { \log 6 }$
D) $\frac { \log 6 } { \log ( a - b ) }$

Question

Quizplus · Accepted Answer

The change of base formula for logarithms is $\log_b(x) = \frac{\log_k(x)}{\log_k(b)}$. Since the base is $1/6$, it becomes $-\frac{\log(a-b)}{\log(6)}$ because $\log_{1/6}(x) = -\log_6(x)$.

Write the Expression Using Only the Indicated Logarithms log⁡1/6(a−b)\log _ { 1 / 6 } ( a - b )log1/6​(a−b)

Write the Expression Using Only the Indicated Logarithms $\log _ { 1 / 6 } ( a - b )$