What is the answer to (9x)^x=9^{3^{18}} ?

The answer to (9x)^x=9^{3^{18}} is x=43046721

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(9x)^x=9^{3^{18}}

(9 x)^{x} = 9^{3^{18}}

x = 43046721

Solution steps

(9 x)^{x} = 9^{3^{18}}

Prepare

(9 x)^{x} = 9^{3^{18}}

for Lambert form:

e^{2 l n (3) (1 - \frac{387420489}{x})} x = 1

Rewrite the equation with

- 2 ln (3) (1 - \frac{387420489}{x}) = u

and

x = \frac{774840978 ln ( 3 )}{u + 2 ln ( 3 )}

e^{- u} (\frac{774840978 ln ( 3 )}{u + 2 ln ( 3 )}) = 1

Solve

e^{- u} (\frac{774840978 ln ( 3 )}{u + 2 ln ( 3 )}) = 1 : u = 16 ln (3)

u = 16 ln (3)

Substitute back

u = - 2 ln (3) (1 - \frac{387420489}{x}),

solve for

x

Solve

- 2 ln (3) (1 - \frac{387420489}{x}) = 16 ln (3) : x = 43046721

x = 43046721

8 (2^{2 x}) - 10 (2^{x}) + 2 = 0

(2)^{x} = 4^{x^{2} + 1}

2^{2 x} + 2^{x + 2} - 12 = 0

- x e^{- x} + e^{- x} = 0

x^{x} = 2^{1000000}

What is the answer to (9x)^x=9^{3^{18}} ?
The answer to (9x)^x=9^{3^{18}} is x=43046721
Solve for x: (9x)^x=9^{3^{18}}
The solution is x=43046721