# Thread: Exponential & Logarithmic Equations

1. ## Exponential & Logarithmic Equations

Confused how to solve this equation:
6 ln(x+2) - 3 = 21

2. ## Re: Exponential & Logarithmic Equations

Originally Posted by paigesisco
Confused how to solve this equation:
6 ln(x+2) - 3 = 21

Can you see that $\ln(x+2)=4~?$

3. ## Re: Exponential & Logarithmic Equations

First, you want to isolate the natural logarithm on one side.

$6 ln(x+2) - 3 = 21$

 Add 3 to both sides of the equations img.top {vertical-align:15%;} $6 ln(x + 2) = 24$ Divide both sides by 6 img.top {vertical-align:15%;} $ln(x + 2) = 4$ Rewrite the equation in exponential form img.top {vertical-align:15%;} $e^4 = x + 2$ Subtract 2 from both sides to solve for x. img.top {vertical-align:15%;} $x = e^4 - 2$

Hope you understood, goodluck!