Use the change-of-base rule to express the given logarithm in terms of common logarithms, in terms of natural logarithms, and correct to four decimal places.
-$\log _{27} 93.10$
$\log 27$

A) $\frac{\log 93.10}{\log 27} ; \frac{\ln 93.10}{\ln 27} ; 1.3756$

B) $\frac{\log 27}{\log 93.10} ; \frac{\ln 27}{\ln 93.10} ; 0.7270$

C) $\frac{\log 93.10}{\log 10} ; \frac{\ln 93.10}{\ln 10} ; 1.9689$

D) $\frac{93.10}{27} ; 3.4481$

Question

Use the change-of-base rule to express the given logarithm in terms of common logarithms, in terms of natural logarithms, and correct to four decimal places.
-$\log _{27} 93.10$
$\log 27$

A) $\frac{\log 93.10}{\log 27} ; \frac{\ln 93.10}{\ln 27} ; 1.3756$

B) $\frac{\log 27}{\log 93.10} ; \frac{\ln 27}{\ln 93.10} ; 0.7270$

C) $\frac{\log 93.10}{\log 10} ; \frac{\ln 93.10}{\ln 10} ; 1.9689$

D) $\frac{93.10}{27} ; 3.4481$

Quizplus · Accepted Answer

The change-of-base formula allows a logarithm to be rewritten as the ratio of two logarithms with a new base. Specifically, $\log_b a = \frac{\log_c a}{\log_c b}$ or $\log_b a = \frac{\ln a}{\ln b}$, where $b$ is the original base, $a$ is the argument of the logarithm, $c$ is the new base, and $\ln$ denotes the natural logarithm. For the given problem, converting $\log_{27} 93.10$ to common logarithms (base 10) and natural logarithms results in $\frac{\log 93.10}{\log 27}$ and $\frac{\ln 93.10}{\ln 27}$, respectively. Calculating these expressions gives a value of approximately 1.3756.

Use the Change-Of-Base Rule to Express the Given Logarithm in Terms