What is the inverse of 3^{x^2-1} ?

The inverse of 3^{x^2-1} is sqrt((ln(3x))/(ln(3))),-sqrt((ln(3x))/(ln(3)))

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inverse of 3^{x^2-1}

inverse

3^{x^{2} - 1}

\frac{ln ( 3 x )}{ln ( 3 )}, - \frac{ln ( 3 x )}{ln ( 3 )}

Solution steps

y = 3^{x^{2} - 1}

Replace

x

with

y

x = 3^{y^{2} - 1}

Solve for

y, x = 3^{y^{2} - 1}

\frac{ln ( 3 x )}{ln ( 3 )}, - \frac{ln ( 3 x )}{ln ( 3 )}

What is the inverse of 3^{x^2-1} ?
The inverse of 3^{x^2-1} is sqrt((ln(3x))/(ln(3))),-sqrt((ln(3x))/(ln(3)))