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Solve 3^(2x - 1) = 2^(1 - x)*36

 Dec 19, 2021
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Solve for x:
3^(2 x - 1) = 9 2^(-x + 3)

Take the natural logarithm of both sides and use the identities log(a b) = log(a) + log(b) and log(a^b) = b log(a):
log(3) (2 x - 1) = log(2) (-x + 3) + 2 log(3)

Expand out terms of the left hand side:
2 log(3) x - log(3) = log(2) (-x + 3) + 2 log(3)

Expand out terms of the right hand side:
2 log(3) x - log(3) = -log(2) x + 3 log(2) + 2 log(3)

Add x log(2) + log(3) to both sides:
(log(2) + 2 log(3)) x = 3 log(2) + 3 log(3)

Divide both sides by log(2) + 2 log(3):

x = (3 log(2) + 3 log(3))/(log(2) + 2 log(3))==~1.85972

 Dec 19, 2021

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