What is the inverse of (2/3)^{x-3}-2 ?

The inverse of (2/3)^{x-3}-2 is (ln(x+2))/(ln(2/3))+3

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inverse of (2/3)^{x-3}-2

inverse

(\frac{2}{3})^{x - 3} - 2

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

Solution steps

y = (\frac{2}{3})^{x - 3} - 2

Replace

x

with

y

x = (\frac{2}{3})^{y - 3} - 2

Solve for

y, x = (\frac{2}{3})^{y - 3} - 2

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

y = \frac{2}{1 \frac{x ^{2}}{4}}

\frac{x + 1}{x + 3}

ln (\frac{x - 1}{x + 1})

x^{10}

\frac{6 x ^{2} - 24}{2 x ^{2} - 4 x}

What is the inverse of (2/3)^{x-3}-2 ?
The inverse of (2/3)^{x-3}-2 is (ln(x+2))/(ln(2/3))+3