What is the answer to 9x27^x=27 ?

The answer to 9x27^x=27 is x=(\W_{0}(9ln(3)))/(3ln(3))

Solve for x: 9x27^x=27

The solution is x=(\W_{0}(9ln(3)))/(3ln(3))

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9 x 2 7^{x} = 27

x = \frac{W _{0} ( 9 ln ( 3 ) )}{3 ln ( 3 )}

Decimal Notation

x = 0.52743 \dots

Solution steps

9 x \cdot 2 7^{x} = 27

Prepare

9 x 2 7^{x} = 27

for Lambert form:

9 x e^{3 l n (3) x} = 27

Rewrite the equation with

3 ln (3) x = u

and

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

9 (\frac{u}{3 ln ( 3 )}) e^{u} = 27

Rewrite

9 (\frac{u}{3 ln ( 3 )}) e^{u} = 27

in Lambert form:

e^{u} u = 9 ln (3)

Solve

e^{u} u = 9 ln (3) : u = W_{0} (9 ln (3))

u = W_{0} (9 ln (3))

Substitute back

u = 3 ln (3) x,

solve for

x

Solve

3 ln (3) x = W_{0} (9 ln (3)) : x = \frac{W _{0} ( 9 ln ( 3 ) )}{3 ln ( 3 )}

x = \frac{W _{0} ( 9 ln ( 3 ) )}{3 ln ( 3 )}

a = 27.2 e^{0.031 t}

79 \cdot 1 0^{5 x} = 78

2^{2 x} - 3 \cdot 2^{x} = 4

e^{0.5 x} = 0.5

(\frac{1}{2})^{x} = \frac{1}{3}

What is the answer to 9x27^x=27 ?
The answer to 9x27^x=27 is x=(\W_{0}(9ln(3)))/(3ln(3))
Solve for x: 9x27^x=27
The solution is x=(\W_{0}(9ln(3)))/(3ln(3))