What is the answer to solvefor x,f(x-9)=8^x ?

The answer to solvefor x,f(x-9)=8^x is x=-(\W(-(402653184ln(2))/f)-27ln(2))/(3ln(2))

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solvefor x,f(x-9)=8^x

solve for

x, f (x - 9) = 8^{x}

x = - \frac{W ( - \frac{402653184 l n ( 2 )}{f} ) - 27 ln ( 2 )}{3 ln ( 2 )}

Solution steps

f (x - 9) = 8^{x}

Prepare

f (x - 9) = 8^{x}

for Lambert form:

f (x - 9) e^{- 3 l n (2) x} = 1

Rewrite the equation with

3 ln (2) (- x + 9) = u

and

x = - \frac{u - 27 ln ( 2 )}{3 ln ( 2 )}

f (- \frac{u - 27 ln ( 2 )}{3 ln ( 2 )} - 9) e^{- 3 l n (2) (- \frac{u - 27 l n ( 2 )}{3 l n ( 2 )})} = 1

Simplify

e^{u - 27 l n (2)} f (- \frac{u - 27 ln ( 2 )}{3 ln ( 2 )} - 9) = 1

Rewrite

e^{u - 27 l n (2)} f (- \frac{u - 27 ln ( 2 )}{3 ln ( 2 )} - 9) = 1

in Lambert form:

e^{u} u = - \frac{402653184 ln ( 2 )}{f}

Solve

e^{u} u = - \frac{402653184 ln ( 2 )}{f} : u = W (- \frac{402653184 ln ( 2 )}{f})

u = W (- \frac{402653184 ln ( 2 )}{f})

Substitute back

u = 3 ln (2) (- x + 9),

solve for

x

Solve

3 ln (2) (- x + 9) = W (- \frac{402653184 ln ( 2 )}{f}) : x = - \frac{W ( - \frac{402653184 l n ( 2 )}{f} ) - 27 ln ( 2 )}{3 ln ( 2 )}

x = - \frac{W ( - \frac{402653184 l n ( 2 )}{f} ) - 27 ln ( 2 )}{3 ln ( 2 )}

5^{x^{2} - 2 x} = 125

8^{\frac{1}{2 x + 2}} = \frac{1}{4}

7^{3 x + 4} = 56

x, 3^{x - 1} = 27

y, x = 5^{y}

What is the answer to solvefor x,f(x-9)=8^x ?
The answer to solvefor x,f(x-9)=8^x is x=-(\W(-(402653184ln(2))/f)-27ln(2))/(3ln(2))