Chapter 11, Problem 6CR

To determine

The solution of the equation $3^x=e$.

Answer to Problem 6CR

Solution:

The solution of the equation $3^x=e$ is $x=\frac{1}{\ln 3}$.

Explanation of Solution

Given information:

The equation $3^x=e$.

Explanation:

Consider the equation, $3^x=e$.

Take natural logarithm function from both sides,

$\ln 3^x=\ln e$

By using $\ln a^M=M\ln a$,

$\Rightarrow x\ln 3=\ln e$

By using, $\ln e=1$,

$\Rightarrow x\ln 3=1$

Dividing both sides by $\ln 3$,

$\Rightarrow x=\frac{1}{\ln 3}$

The solution of the equation $3^x=e$ is $x=\frac{1}{\ln 3}$.