2^2x-5=3^4x

Question

Can you please go through the problem step by step, explaining every detail, including the properties used in each step? Thanks!(:

Answer 1

2^2x-5=3^4x.

Take logs of each side:

(2x-5)log(2)=4xlog(3),

2xlog(2)-5log(2)=4xlog(3),

2xlog(2)-4xlog(3)=5log(2),

x(2log(2)-4log(3))=5log(2),

xlog(2²/3⁴)=5log(2),

x=5log(2)/log(4/81)=-1.1521 approx.