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

1 Answer
Gió
Dec 19, 2015

I found #x=0.13614#

Explanation:

We can try taking the natural log of both sides:
#ln(3^(2-x))=ln(5^(2x+1))#
then use the property of logs:
#logx^y=ylogx# to write:
#(2-x)ln(3)=(2x+1)ln(5)#
#2ln(3)-xln(3)=2xln(5)+ln(5)#
collecting #x#:
#x(2ln(5)+ln(3))=2ln(3)-ln(5)#
so:
#x=(2ln(3)-ln(5))/(2ln(5)+ln(3))=0.13614#

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