Answer:
f(x) = -2x + 1
Step-by-step explanation:
The given expression is [tex]\frac{64^x}{4^{5x-1}}[/tex]
By solving the given expression further,
[tex]\frac{64^x}{4^{5x-1}}[/tex] = [tex]\frac{[(4)^{3}]^x}{(4)^{5x-1}}[/tex] [Since 64 = 4³]
= [tex]\frac{4^{3x}}{4^{5x-1}}[/tex]
= [tex]4^{3x}\times 4^{-(5x-1)}[/tex] [Since [tex]\frac{1}{a}=a^{-1}[/tex]]
= [tex]4^{3x-5x+1}[/tex] [Since [tex]a^x\times a^y=a^{(x+y)}[/tex]]
= [tex]4^{(-2x+1)}[/tex]
By comparing the result with [tex]4^{\text{f(x)}}[/tex]
f(x) = -2x + 1
Therefore, f(x) = (-2x + 1) will be the answer.