What is the answer to (x+2)^{x+2}=216^2 ?

The answer to (x+2)^{x+2}=216^2 is x=4

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(x+2)^{x+2}=216^2

(x + 2)^{x + 2} = 21 6^{2}

x = 4

Solution steps

(x + 2)^{x + 2} = 21 6^{2}

Prepare

(x + 2)^{x + 2} = 21 6^{2}

for Lambert form:

(x + 2) e^{- \frac{6 l n ( 6 )}{x + 2}} = 1

Rewrite the equation with

\frac{6 ln ( 6 )}{x + 2} = u

and

x = \frac{6 ln ( 6 )}{u} - 2

((\frac{6 ln ( 6 )}{u} - 2) + 2) e^{- u} = 1

Rewrite

((\frac{6 ln ( 6 )}{u} - 2) + 2) e^{- u} = 1

in Lambert form:

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

Solve

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

u = ln (6)

Substitute back

u = \frac{6 ln ( 6 )}{x + 2},

solve for

x

Solve

\frac{6 ln ( 6 )}{x + 2} = ln (6) : x = 4

x = 4

6 e^{- 4 k - 10} = 67

e^{3 x + 2} = e^{3}

3^{x} (5^{2 x}) = 6 (2^{x})

2^{x} - 2^{x - 2} = 6

1 0^{2 - b} = 10000

What is the answer to (x+2)^{x+2}=216^2 ?
The answer to (x+2)^{x+2}=216^2 is x=4
Solve for x: (x+2)^{x+2}=216^2
The solution is x=4