Exponential & Logarithmic Equations

**paigesisco** · March 15th 2013, 08:35 AM

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

**Plato** · March 15th 2013, 08:38 AM

Originally Posted by paigesisco

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

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

**ReneG** · March 16th 2013, 10:02 AM

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

Hope you understood, goodluck!

Thread: Exponential & Logarithmic Equations