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}

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}