What is the inverse of f(x)=((9^x)^{1/2})/5 ?

The inverse of f(x)=((9^x)^{1/2})/5 is (ln(x*5))/(ln(3))

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inverse of f(x)=((9^x)^{1/2})/5

inverse

f (x) = \frac{( 9 ^{x} ) ^{\frac{1}{2}}}{5}

\frac{ln ( x \cdot 5 )}{ln ( 3 )}

Solution steps

y = \frac{( 9 ^{x} ) ^{\frac{1}{2}}}{5}

Replace

x

with

y

x = \frac{( 9 ^{y} ) ^{\frac{1}{2}}}{5}

Solve for

y, x = \frac{( 9 ^{y} ) ^{\frac{1}{2}}}{5}

\frac{ln ( x \cdot 5 )}{ln ( 3 )}

What is the inverse of f(x)=((9^x)^{1/2})/5 ?
The inverse of f(x)=((9^x)^{1/2})/5 is (ln(x*5))/(ln(3))