What is the answer to x6^{x-8}=7 ?

The answer to x6^{x-8}=7 is x=(\W_{0}(11757312ln(6)))/(ln(6))

Solve for x: x6^{x-8}=7

The solution is x=(\W_{0}(11757312ln(6)))/(ln(6))

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x 6^{x - 8} = 7

x = \frac{W _{0} ( 11757312 ln ( 6 ) )}{ln ( 6 )}

Decimal Notation

x = 7.93035 \dots

Solution steps

x \cdot 6^{x - 8} = 7

Prepare

x 6^{x - 8} = 7

for Lambert form:

x e^{l n (6) (x - 8)} = 7

Rewrite the equation with

x ln (6) = u

and

x = \frac{u}{ln ( 6 )}

(\frac{u}{ln ( 6 )}) e^{l n (6) ((\frac{u}{l n ( 6 )}) - 8)} = 7

Simplify

\frac{e ^{u - 8 l n (6)} u}{ln ( 6 )} = 7

Rewrite

\frac{e ^{u - 8 l n (6)} u}{ln ( 6 )} = 7

in Lambert form:

e^{u} u = 11757312 ln (6)

Solve

e^{u} u = 11757312 ln (6) : u = W_{0} (11757312 ln (6))

u = W_{0} (11757312 ln (6))

Substitute back

u = x ln (6),

solve for

x

Solve

x ln (6) = W_{0} (11757312 ln (6)) : x = \frac{W _{0} ( 11757312 ln ( 6 ) )}{ln ( 6 )}

x = \frac{W _{0} ( 11757312 ln ( 6 ) )}{ln ( 6 )}

3^{2 x - 3} = 27 \frac{x + 1}{3}

(2 e^{- x} x - e^{- x} x^{2}) = 0

1 0^{y + 1} = e^{2} lo g_{10} (e)

6 4^{- x} = 4

2^{x + 2} + 2^{x - 3} = 66

What is the answer to x6^{x-8}=7 ?
The answer to x6^{x-8}=7 is x=(\W_{0}(11757312ln(6)))/(ln(6))
Solve for x: x6^{x-8}=7
The solution is x=(\W_{0}(11757312ln(6)))/(ln(6))