What is the inverse of f(x)=100(2)^{x/3} ?

The inverse of f(x)=100(2)^{x/3} is (3ln(x/(100)))/(ln(2))

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inverse of f(x)=100(2)^{x/3}

inverse

f (x) = 100 (2)^{\frac{x}{3}}

\frac{3 ln ( \frac{x}{100} )}{ln ( 2 )}

Solution steps

y = 100 \cdot 2^{\frac{x}{3}}

Replace

x

with

y

x = 100 \cdot 2^{\frac{y}{3}}

Solve for

y, x = 100 2^{\frac{y}{3}}

\frac{3 ln ( \frac{x}{100} )}{ln ( 2 )}

What is the inverse of f(x)=100(2)^{x/3} ?
The inverse of f(x)=100(2)^{x/3} is (3ln(x/(100)))/(ln(2))