What is the inverse of 2^{x^2+2x} ?

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

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inverse of 2^{x^2+2x}

inverse

2^{x^{2} + 2 x}

\frac{- ln ( 2 ) + ln ( 2 ) ln ( 2 x )}{ln ( 2 )}, - \frac{ln ( 2 ) ln ( 2 x ) + ln ( 2 )}{ln ( 2 )}

Solution steps

y = 2^{x^{2} + 2 x}

Replace

x

with

y

x = 2^{y^{2} + 2 y}

Solve for

y, x = 2^{y^{2} + 2 y}

\frac{- ln ( 2 ) + ln ( 2 ) ln ( 2 x )}{ln ( 2 )}, - \frac{ln ( 2 ) ln ( 2 x ) + ln ( 2 )}{ln ( 2 )}

f (x) = 7 + x - 7

\frac{7 x - 5}{11}

lo g_{9} (2)

3 - x + 5

2 lo g_{10} (3 x - 4)

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