What is the inverse of 5*2^{1-x}-1 ?

The inverse of 5*2^{1-x}-1 is -(ln((x+1)/5)-ln(2))/(ln(2))

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inverse of 5*2^{1-x}-1

inverse

5 \cdot 2^{1 - x} - 1

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

Solution steps

y = 5 \cdot 2^{1 - x} - 1

Replace

x

with

y

x = 5 \cdot 2^{1 - y} - 1

Solve for

y, x = 5 \cdot 2^{1 - y} - 1

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

f (x) = ln (sin (x))

f (x) = 5 ln (2 x) + 3

f (x) = 2 (5^{x} - 8)

y = - 1 - x + 3

g (x) = \frac{x - 1}{2}

What is the inverse of 5*2^{1-x}-1 ?
The inverse of 5*2^{1-x}-1 is -(ln((x+1)/5)-ln(2))/(ln(2))