Question

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

Answer 1

`e^(3x)=12\\\\3x=\ln 12\\\\x=(\ln 12)/(3)\approx0.83\\\\\\`

Answer 2

x=0.83

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=(\ln 12)/(3)`
`\text{divides both sides by 3}`

The exact value of x is
`(\ln 12)/(3)`

Using calculator to find ln 12

`x=(2.4849)/(3)`

`x=0.8283`

Hence, The value of x is 0.83