What is the inverse of f(x)= 1/3 log_{10}(5x) ?

The inverse of f(x)= 1/3 log_{10}(5x) is 8^x*5^{3x-1}

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inverse of f(x)= 1/3 log_{10}(5x)

inverse

f (x) = \frac{1}{3} lo g_{10} (5 x)

8^{x} \cdot 5^{3 x - 1}

Solution steps

y = \frac{1}{3} lo g_{10} (5 x)

Replace

x

with

y

x = \frac{1}{3} lo g_{10} (5 y)

Solve for

y, x = \frac{1}{3} lo g_{10} (5 y)

8^{x} \cdot 5^{3 x - 1}

y = - 35 x - 46.716

f (x) = \frac{x ^{2} + 4 x - 5}{x ^{2} - 7 x + 6}

5 + 2 x

\frac{1}{2} ln (x^{2} - 2 x - 1)

\frac{1}{\frac{6}{5} x - 9}

What is the inverse of f(x)= 1/3 log_{10}(5x) ?
The inverse of f(x)= 1/3 log_{10}(5x) is 8^x*5^{3x-1}