What is the inverse of f(x)=7^{log_{7}(x-1)} ?

The inverse of f(x)=7^{log_{7}(x-1)} is 7^{(ln(x))/(ln(7))}+1

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inverse of f(x)=7^{log_{7}(x-1)}

inverse

f (x) = 7^{l o g_{7} (x - 1)}

7^{\frac{l n ( x )}{l n ( 7 )}} + 1

Solution steps

y = 7^{l o g_{7} (x - 1)}

Replace

x

with

y

x = 7^{l o g_{7} (y - 1)}

Solve for

y, x = 7^{l o g_{7} (y - 1)}

7^{\frac{l n ( x )}{l n ( 7 )}} + 1

What is the inverse of f(x)=7^{log_{7}(x-1)} ?
The inverse of f(x)=7^{log_{7}(x-1)} is 7^{(ln(x))/(ln(7))}+1