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Popular >

a^a=27

Solution

a^{a} = 27

Solution

a = 3

Solution steps

a^{a} = 27

Prepare

a^{a} = 27

for Lambert form:

a e^{- \frac{3 l n ( 3 )}{a}} = 1

Rewrite the equation with

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

and

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

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

Rewrite

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

in Lambert form:

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

Solve

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

Verify Solutions:

u = ln (3)

True

The solution is

u = ln (3)

Substitute back

u = \frac{3 ln ( 3 )}{a},

solve for

a

Solve

\frac{3 ln ( 3 )}{a} = ln (3) : a = 3

a = 3

Popular Examples

63 = 1 3^{x}

2^{x} + 2^{x - 1} = 12

3^{2x-2}=sqrt(3)

3^{2 x - 2} = 3

solvefor x,e^x+e^{-x}=2y solve for

x, e^{x} + e^{- x} = 2 y

(3^1)/x =(27^x)^2

\frac{3 ^{1}}{x} = (2 7^{x})^{2}

Frequently Asked Questions (FAQ)

What is the answer to a^a=27 ?
The answer to a^a=27 is a=3
Solve for a: a^a=27
The solution is a=3