# 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 $\displaystyle \ln(x+2)=4~?$

3. ## Re: Exponential & Logarithmic Equations

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

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

 Add 3 to both sides of the equations $\displaystyle 6 ln(x + 2) = 24$ Divide both sides by 6 $\displaystyle ln(x + 2) = 4$ Rewrite the equation in exponential form $\displaystyle e^4 = x + 2$ Subtract 2 from both sides to solve for x. $\displaystyle x = e^4 - 2$

Hope you understood, goodluck!