Answer: x = [tex]\frac{-5}{2}[/tex]
Step-by-step explanation:
[tex]3^{4x-5}[/tex] = [tex](\frac{1}{27}) ^{2x+10}[/tex]
1/27 can be written in index form as [tex]3^{-3}[/tex]
The equation then becomes:
[tex]3^{4x-5}[/tex] = [tex](3^{-3})^{2x+10}[/tex]
Equating the coefficient
4x - 5 = -3 ( 2x + 10)
4x - 5 = -6x - 30
10x = -30 + 5
10x = -25
x = -25/10
x = -5/2
x = - 2.5
