Respuesta :
The expression for f(x), when we rewrite [tex]\frac{64^x}{4^{5x-1}}[/tex] as [tex]4^{f(x)}[/tex] will be [tex]4^{-2x+1}[/tex].
What is expression ?
Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
[tex]\frac{64^x}{4^{5x-1}}[/tex]
So,
Now, to rewrite in form of [tex]4^{f(x)}[/tex],
So,
Rewrite the given expression in the form of 4,
i.e.
[tex]\frac{64^x}{4^{5x-1}}[/tex]
[tex]=\frac{(4^3)^x}{4^{5x-1}}[/tex]
[tex]=\frac{(4^3x)}{4^{5x-1}}[/tex]
NOw,
Using Exponent rule,
We get,
[tex]=4^{3x-(5x-1)}=4^{3x-5x+1}[/tex]
On solving we get,
[tex]=4^{-2x+1}[/tex]
So,
[tex]4^{f(x)}=4^{-2x+1}[/tex]
Hence, we can say that the expression for f(x), when we rewrite [tex]\frac{64^x}{4^{5x-1}}[/tex] as [tex]4^{f(x)}[/tex] will be [tex]4^{-2x+1}[/tex].
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