How can I find X? (Exponential Equation)

Question

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

1478 views around the world

You can reuse this answer
Creative Commons License

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:

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