What is the inverse of f(x)=log_{1/4}(x^5) ?

The inverse of f(x)=log_{1/4}(x^5) is (1/4)^{x/5}

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inverse of f(x)=log_{1/4}(x^5)

inverse

f (x) = lo g_{\frac{1}{4}} (x^{5})

(\frac{1}{4})^{\frac{x}{5}}

Solution steps

y = lo g_{\frac{1}{4}} (x^{5})

Replace

x

with

y

x = lo g_{\frac{1}{4}} (y^{5})

Solve for

y, x = lo g_{\frac{1}{4}} (y^{5})

(\frac{1}{4})^{\frac{x}{5}}

f (x) = 2 cos (3 x) + 1

\frac{1}{6} x^{3} - 3

y = 5 x - 3

f (x) = 2^{- x}

\frac{5}{9} (x - 32)

What is the inverse of f(x)=log_{1/4}(x^5) ?
The inverse of f(x)=log_{1/4}(x^5) is (1/4)^{x/5}