What is the inverse of f(x)=2^{5x+7} ?

The inverse of f(x)=2^{5x+7} is (ln(x)-7ln(2))/(5ln(2))

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inverse of f(x)=2^{5x+7}

inverse

f (x) = 2^{5 x + 7}

\frac{ln ( x ) - 7 ln ( 2 )}{5 ln ( 2 )}

Solution steps

y = 2^{5 x + 7}

Replace

x

with

y

x = 2^{5 y + 7}

Solve for

y, x = 2^{5 y + 7}

\frac{ln ( x ) - 7 ln ( 2 )}{5 ln ( 2 )}

f (x) = 2 (x - 0.75) - 2.125

f (x) = 0. 2^{x}

lo g_{10} (3 x)

f (x) = \frac{x ^{2}}{x ^{2} - 4}

\frac{1 + x}{x - 1}

What is the inverse of f(x)=2^{5x+7} ?
The inverse of f(x)=2^{5x+7} is (ln(x)-7ln(2))/(5ln(2))