How do you solve for x in 3ln3x=6?

1 Answer
Dec 31, 2015

x=e23

Explanation:

Method One

Divide both sides by 3.

ln3x=2

To undo the natural logarithm, exponentiate both sides with base e.

eln3x=e2

3x=e2

x=e23

Method Two

Rewrite the original expression using logarithm rules.

ln((3x)3)=6

ln(27x3)=6

eln(27x3)=e6

27x3=e6

x3=e627

(x3)13=(e2)33313

x=e23