#1**0 **

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**

Guest Dec 19, 2021