Rewrite the logarithm as a ratio of natural logarithms. $\log _ { x } \frac { 5 } { 11 }$
A) $\frac { \ln \frac { 5 } { 11 } } { \ln x }$
B) $\ln \frac { 11 } { 5 x }$
C) $\ln \frac { 5 } { 11 } x$
D) $\frac { \ln x } { \ln \frac { 5 } { 11 } }$
E)None of these

Question

Rewrite the logarithm as a ratio of natural logarithms. $\log _ { x } \frac { 5 } { 11 }$ 
A) $\frac { \ln \frac { 5 } { 11 } } { \ln x }$
B) $\ln \frac { 11 } { 5 x }$
C) $\ln \frac { 5 } { 11 } x$
D) $\frac { \ln x } { \ln \frac { 5 } { 11 } }$
E)None of these

Quizplus · Accepted Answer

The change of base formula for logarithms states that $\log _ { a } b = \frac { \ln b } { \ln a }$. Applying this formula to $\log _ { x } \frac { 5 } { 11 }$ gives $\frac { \ln \frac { 5 } { 11 } } { \ln x }$.

Rewrite the Logarithm as a Ratio of Natural Logarithms log⁡x511\log _ { x } \frac { 5 } { 11 }logx​115​

Rewrite the Logarithm as a Ratio of Natural Logarithms $\log _ { x } \frac { 5 } { 11 }$