# How can I find X? (Exponential Equation)

##
#2^(3x+1) = 3^(x-2)#

##### 1 Answer

Apr 13, 2017

#### Explanation:

Given:

#2^(3x+1) = 3^(x-2)#

Take logs of both sides to get:

#(3x+1)ln 2 = (x-2)ln3#

Multiply out to get:

#(3 ln 2)x + ln 2 = (ln 3)x- 2 ln 3#

Subtract

#(3 ln 2 - ln 3)x = - ln 2 - 2 ln 3#

Divide both sides by

#x = -(ln 2 + 2 ln 3)/(3 ln 2 - ln 3)#