Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$3 ^ { 9 x } = 2.3$$
A) $\left\{ \frac { \ln 2.3 } { 9 \ln 3 } \right\}$
B) $\left\{ \frac { \ln 2.3 } { 3 \ln 9 } \right\}$
C) $\left\{ \frac { 9 \ln 2.3 } { \ln 3 } \right\}$
D) $\left\{ \frac { 2.3 \ln 9 } { \ln 3 } \right\}$

Question

Quizplus · Accepted Answer

We take the natural logarithm of both sides to get $\ln(3^{9x}) = \ln 2.3$. Using the properties of logarithms, we can simplify the left side to $9x\ln 3$. Thus, we have $9x\ln 3 = \ln 2.3$. Solving for $x$, we get $x = \frac{\ln 2.3}{9\ln 3}$. Therefore, the solution set is $\left\{ \frac{\ln 2.3}{9\ln 3}\right\}$.

Solve the Exponential Equation 39x=2.33 ^ { 9 x } = 2.339x=2.3

Solve the Exponential Equation $3 ^ { 9 x } = 2.3$