What is the answer to 64x8^x=8^{11} ?

The answer to 64x8^x=8^{11} is x=8

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64x8^x=8^{11}

64 x 8^{x} = 8^{11}

x = 8

Solution steps

64 x \cdot 8^{x} = 8^{11}

Prepare

64 x 8^{x} = 8^{11}

for Lambert form:

64 x e^{3 l n (2) x} = 8^{11}

Rewrite the equation with

3 ln (2) x = u

and

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

64 (\frac{u}{3 ln ( 2 )}) e^{u} = 8^{11}

Rewrite

64 (\frac{u}{3 ln ( 2 )}) e^{u} = 8^{11}

in Lambert form:

e^{u} u = 402653184 ln (2)

Solve

e^{u} u = 402653184 ln (2) : u = 24 ln (2)

u = 24 ln (2)

Substitute back

u = 3 ln (2) x,

solve for

x

Solve

3 ln (2) x = 24 ln (2) : x = 8

x = 8

5^{x} = 50

2^{2 x} - 3 \cdot 2^{x} = - 2

6 4^{- x + 26} = 12 8^{x}

5^{x} = 6^{x - 1}