What is the inverse of f(x)=1+5log_{2}(x-3) ?

The inverse of f(x)=1+5log_{2}(x-3) is 2^{(x-1)/5}+3

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inverse of f(x)=1+5log_{2}(x-3)

inverse

f (x) = 1 + 5 lo g_{2} (x - 3)

2^{\frac{x - 1}{5}} + 3

Solution steps

y = 1 + 5 lo g_{2} (x - 3)

Replace

x

with

y

x = 1 + 5 lo g_{2} (y - 3)

Solve for

y, x = 1 + 5 lo g_{2} (y - 3)

2^{\frac{x - 1}{5}} + 3

f (x) = - \frac{6}{11} x

g (x) = \frac{9}{x - 6}

f (x) = 5 - x + x^{2} - 1

\frac{2 x ^{3} + 3}{x ^{3} - 1}

f (x) = \frac{x - 1}{x - 2}

What is the inverse of f(x)=1+5log_{2}(x-3) ?
The inverse of f(x)=1+5log_{2}(x-3) is 2^{(x-1)/5}+3