What is the inverse of f(x)=log_{10}(4^{x+2}) ?

The inverse of f(x)=log_{10}(4^{x+2}) is (xln(10))/(2ln(2))-2

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inverse of f(x)=log_{10}(4^{x+2})

inverse

f (x) = lo g_{10} (4^{x + 2})

\frac{x ln ( 10 )}{2 ln ( 2 )} - 2

Solution steps

y = lo g_{10} (4^{x + 2})

Replace

x

with

y

x = lo g_{10} (4^{y + 2})

Solve for

y, x = lo g_{10} (4^{y + 2})

\frac{x ln ( 10 )}{2 ln ( 2 )} - 2

f (x) = 1 - (x - 1)^{2}

f (x) = \frac{x}{22}

4^{x + 3} - 2

\frac{6 s - 5}{s ^{2} + 7}

\frac{3}{9 s ^{2} + 12 s + 13}

What is the inverse of f(x)=log_{10}(4^{x+2}) ?
The inverse of f(x)=log_{10}(4^{x+2}) is (xln(10))/(2ln(2))-2