What is the inverse of f(x)= 1/3 log_{10}(2x) ?

The inverse of f(x)= 1/3 log_{10}(2x) is 125^x*2^{3x-1}

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inverse of f(x)= 1/3 log_{10}(2x)

inverse

f (x) = \frac{1}{3} lo g_{10} (2 x)

12 5^{x} \cdot 2^{3 x - 1}

Solution steps

y = \frac{1}{3} lo g_{10} (2 x)

Replace

x

with

y

x = \frac{1}{3} lo g_{10} (2 y)

Solve for

y, x = \frac{1}{3} lo g_{10} (2 y)

12 5^{x} \cdot 2^{3 x - 1}

What is the inverse of f(x)= 1/3 log_{10}(2x) ?
The inverse of f(x)= 1/3 log_{10}(2x) is 125^x*2^{3x-1}