What is the inverse of f(x)=(3^{x-2})/5 ?

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

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inverse of f(x)=(3^{x-2})/5

inverse

f (x) = \frac{3 ^{x - 2}}{5}

\frac{ln ( x \cdot 5 )}{ln ( 3 )} + 2

Solution steps

y = \frac{3 ^{x - 2}}{5}

Replace

x

with

y

x = \frac{3 ^{y - 2}}{5}

Solve for

y, x = \frac{3 ^{y - 2}}{5}

\frac{ln ( x \cdot 5 )}{ln ( 3 )} + 2

x - 3 + 9

f (x) = 2 x^{2} - 12 x + 5

y = lo g_{2} (4 x)

f (x) = lo g_{3} (2 x + 4) - 6

f (x) = \frac{7 x + 6}{x - 5}

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