What is the inverse of y=4^x-5*2^x+6 ?

The inverse of y=4^x-5*2^x+6 is (ln((5+sqrt(4x+1))/2))/(ln(2)),(ln((5-sqrt(4x+1))/2))/(ln(2))

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inverse of y=4^x-5*2^x+6

inverse

y = 4^{x} - 5 \cdot 2^{x} + 6

\frac{ln ( \frac{5 + 4 x + 1}{2} )}{ln ( 2 )}, \frac{ln ( \frac{5 - 4 x + 1}{2} )}{ln ( 2 )}

Solution steps

y = 4^{x} - 5 \cdot 2^{x} + 6

Replace

x

with

y

x = 4^{y} - 5 \cdot 2^{y} + 6

Solve for

y, x = 4^{y} - 5 \cdot 2^{y} + 6

\frac{ln ( \frac{5 + 4 x + 1}{2} )}{ln ( 2 )}, \frac{ln ( \frac{5 - 4 x + 1}{2} )}{ln ( 2 )}

What is the inverse of y=4^x-5*2^x+6 ?
The inverse of y=4^x-5*2^x+6 is (ln((5+sqrt(4x+1))/2))/(ln(2)),(ln((5-sqrt(4x+1))/2))/(ln(2))