Use the Definition of a Logarithm to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$3 \ln ( 6 x ) = 6$
A) $\left\{ \frac { e ^ { 2 } } { 6 } \right\}$
B) $\left\{ e ^ { 1 / 3 } \right\}$
C) $\left\{ e ^ { 2 } \right\}$
D) $\left\{ \frac { 2 } { \ln 6 } \right\}$

Question

Quizplus · Accepted Answer

Divide both sides by 3 to get $\ln(6x) = 2$. Using the definition of a logarithm, convert to exponential form: $e^2 = 6x$. Solve for $x$ to get $x = \frac{e^2}{6}$.

Use the Definition of a Logarithm to Solve Logarithmic Equations 3ln⁡(6x)=63 \ln ( 6 x ) = 63ln(6x)=6

Use the Definition of a Logarithm to Solve Logarithmic Equations $3 \ln ( 6 x ) = 6$