What is the inverse of 6log_{2}(2^x-7) ?

The inverse of 6log_{2}(2^x-7) is (ln(2^{x/6}+7))/(ln(2))

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inverse of 6log_{2}(2^x-7)

inverse

6 lo g_{2} (2^{x} - 7)

\frac{ln ( 2 ^{\frac{x}{6}} + 7 )}{ln ( 2 )}

Solution steps

y = 6 lo g_{2} (2^{x} - 7)

Replace

x

with

y

x = 6 lo g_{2} (2^{y} - 7)

Solve for

y, x = 6 lo g_{2} (2^{y} - 7)

\frac{ln ( 2 ^{\frac{x}{6}} + 7 )}{ln ( 2 )}

What is the inverse of 6log_{2}(2^x-7) ?
The inverse of 6log_{2}(2^x-7) is (ln(2^{x/6}+7))/(ln(2))