How can I find X? (Exponential Equation)

Question

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

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Answer 1 · 2017-04-13T13:13:20

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

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 #ln 2 + (ln 3)x# from both sides to get:

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

Divide both sides by #(3 ln 2 - ln 3)# to get:

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