What is the inverse of f(x)= 1/4*10^{x-3}+5 ?

The inverse of f(x)= 1/4*10^{x-3}+5 is (ln(4x-20))/(ln(10))+3

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inverse of f(x)= 1/4*10^{x-3}+5

inverse

f (x) = \frac{1}{4} \cdot 1 0^{x - 3} + 5

\frac{ln ( 4 x - 20 )}{ln ( 10 )} + 3

Solution steps

y = \frac{1}{4} \cdot 1 0^{x - 3} + 5

Replace

x

with

y

x = \frac{1}{4} \cdot 1 0^{y - 3} + 5

Solve for

y, x = \frac{1}{4} \cdot 1 0^{y - 3} + 5

\frac{ln ( 4 x - 20 )}{ln ( 10 )} + 3

f (x) = \frac{1}{1 + y ^{3}}

f (x) = \frac{y + 4}{2 y - 5}

f (x) = 14 - \frac{( 1 + 10 )}{3}

- 3 x^{2} - 4 x + 4

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

What is the inverse of f(x)= 1/4*10^{x-3}+5 ?
The inverse of f(x)= 1/4*10^{x-3}+5 is (ln(4x-20))/(ln(10))+3