How do you solve #3^(2x−1) = 5^(2−3x)#?

1 Answer
Gió
Nov 28, 2015

I found: #x=0.61454#

Explanation:

Take the natural log of both sides:
#ln3^(2x-1)=ln5^(2-3x)#
use the property of logs:
#logx^a=alogx#
#(2x-1)ln3=(2-3x)ln5#
#2(ln3)x-ln3=2ln5-3(ln5)x#
collect #x#:
#x[2(ln3)+3(ln5)]=2ln5+ln3#
#x[7.02554]=4.31748#
#x=4.31748/7.02554=0.61454#

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