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

1 Answer
Gió
Dec 31, 2015

I found #-3.2116#

Explanation:

We can take the natural log of both sides:
#ln(5)^(x-2)=ln(3)^(3x+2)#
We use the property of the logs:
#logx^y=ylogx#
#(x-2)ln(5)=(3x+2)ln(3)#
Rearrange:
#xln5-2ln5=3xln3+2ln3#
#x(ln5-3ln3)=2ln5+2ln3#
#x=(2ln5+2ln3)/(ln5-3ln3)=-3.2116#

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