What is the inverse of f(x)=6log_{10}(0.5x) ?

The inverse of f(x)=6log_{10}(0.5x) is 5^{x/6}*2^{x/6+1}

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inverse of f(x)=6log_{10}(0.5x)

inverse

f (x) = 6 lo g_{10} (0.5 x)

5^{\frac{x}{6}} \cdot 2^{\frac{x}{6} + 1}

Solution steps

y = 6 lo g_{10} (0.5 x)

Replace

x

with

y

x = 6 lo g_{10} (0.5 y)

Solve for

y, x = 6 lo g_{10} (0.5 y)

5^{\frac{x}{6}} \cdot 2^{\frac{x}{6} + 1}

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

f (x) = \frac{x + 4}{x ^{2} - 36}

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

y = lo g_{5} (x)

0.001 x^{3} + 4 x + 686

What is the inverse of f(x)=6log_{10}(0.5x) ?
The inverse of f(x)=6log_{10}(0.5x) is 5^{x/6}*2^{x/6+1}