What is the answer to (m-2)^{m-2}=144^6 ?

The answer to (m-2)^{m-2}=144^6 is m=14

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(m-2)^{m-2}=144^6

(m - 2)^{m - 2} = 14 4^{6}

m = 14

Solution steps

(m - 2)^{m - 2} = 14 4^{6}

Prepare

(m - 2)^{m - 2} = 14 4^{6}

for Lambert form:

(m - 2) e^{- \frac{12 l n ( 12 )}{m - 2}} = 1

Rewrite the equation with

\frac{12 ln ( 12 )}{m - 2} = u

and

m = \frac{12 ln ( 12 )}{u} + 2

((\frac{12 ln ( 12 )}{u} + 2) - 2) e^{- u} = 1

Rewrite

((\frac{12 ln ( 12 )}{u} + 2) - 2) e^{- u} = 1

in Lambert form:

u e^{u} = 12 ln (12)

Solve

u e^{u} = 12 ln (12) : u = ln (12)

u = ln (12)

Substitute back

u = \frac{12 ln ( 12 )}{m - 2},

solve for

m

Solve

\frac{12 ln ( 12 )}{m - 2} = ln (12) : m = 14

m = 14

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

5^{b} = 2 5^{b} - 1

2 e^{y} + 15 e^{- y} = 11

2.16 = (1 + 0.12)^{n - 1}

x^{a} = e^{x - 1}

What is the answer to (m-2)^{m-2}=144^6 ?
The answer to (m-2)^{m-2}=144^6 is m=14
Solve for m: (m-2)^{m-2}=144^6
The solution is m=14