Question

What is the solution to the equation e^3x=12 Round your answer to the nearest hundredth.

Answer 1

Answer:

x=0.83

Step-by-step explanation:

Given: $e^{3x}=12$

We are given an exponential equation and to solve for x.

$e^{3x}=12$

Taking ln both sides

$\ln e^{3x}=\ln 12$

$3x\ln e=\ln 12$                        $\because ln a^m=m\ln a$

$3x=\ln 12$                            $\because \ln e=1$

$x=\dfrac{\ln 12}{3}$                   $\text{divides both sides by 3}$

The exact value of x is $\dfrac{\ln 12}{3}$    

Using calculator to find ln 12

$x=\dfrac{2.4849}{3}$

$x=0.8283$

Hence, The value of x is 0.83

Answer 2

$e^{3x}=12\\\\3x=\ln 12\\\\x=\dfrac{\ln 12}{3}\approx0.83$