Rewrite the logarithm as a ratio of common logarithms. $\log _ { x } \frac { 2 } { 11 }$
A) $\frac { \log x } { \log \frac { 2 } { 11 } }$
B) $\frac { \log \frac { 2 } { 11 } } { \log x }$
C) $\log \frac { 2 } { 11 } x$
D) $\log \frac { 11 } { 2 x }$
E)None of these

Question

Rewrite the logarithm as a ratio of common logarithms.  $\log _ { x } \frac { 2 } { 11 }$ 
A) $\frac { \log x } { \log \frac { 2 } { 11 } }$
B) $\frac { \log \frac { 2 } { 11 } } { \log x }$
C) $\log \frac { 2 } { 11 } x$
D) $\log \frac { 11 } { 2 x }$
E)None of these

Quizplus · Accepted Answer

The correct answer is obtained by applying the change of base formula for logarithms, which is $\log_b a = \frac{\log_c a}{\log_c b}$, where $a$ and $b$ are positive real numbers, and $b \neq 1$. Applying this formula to the given logarithm $\log_x \frac{2}{11}$ with a common logarithm base (usually 10), we get $\frac{\log \frac{2}{11}}{\log x}$.

Rewrite the Logarithm as a Ratio of Common Logarithms log⁡x211\log _ { x } \frac { 2 } { 11 }logx​112​

Rewrite the Logarithm as a Ratio of Common Logarithms $\log _ { x } \frac { 2 } { 11 }$