Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 \left( 3 ^ { x } \right) = 36$
A) $\frac { \ln 18 } { \ln 3 } \approx 0.380$
B) $\frac { \ln 18 } { \ln 3 } \approx - 0.380$
C) $\frac { \ln 18 } { \ln 3 } \approx - 2.631$
D) $\frac { \ln 3 } { \ln 18 } \approx 2.631$
E) $\frac { \ln 18 } { \ln 3 } \approx 2.631$

Question

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $2 \left( 3 ^ { x } \right) = 36$ ​
A) $\frac { \ln 18 } { \ln 3 } \approx 0.380$
B) $\frac { \ln 18 } { \ln 3 } \approx - 0.380$
C) $\frac { \ln 18 } { \ln 3 } \approx - 2.631$
D) $\frac { \ln 3 } { \ln 18 } \approx 2.631$
E) $\frac { \ln 18 } { \ln 3 } \approx 2.631$

Quizplus · Accepted Answer

First, simplify the equation: $2(3^x) = 36$ becomes $3^x = 18$. Taking the natural logarithm of both sides gives $x \ln(3) = \ln(18)$, so $x = \frac{\ln(18)}{\ln(3)}$. Calculating this gives approximately 2.631.

Solve the Exponential Equation Algebraically 2(3x)=362 \left( 3 ^ { x } \right) = 362(3x)=36

Solve the Exponential Equation Algebraically $2 \left( 3 ^ { x } \right) = 36$