What is the answer to (x-2)^{x^2-2x}=(x-2)^{x+4} ?

The answer to (x-2)^{x^2-2x}=(x-2)^{x+4} is x=3,x=4

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

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

x = 3, x = 4

Solution steps

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

Apply exponent rules

(x^{2} - 2 x) ln (x - 2) = (x + 4) ln (x - 2)

Solve

(x^{2} - 2 x) ln (x - 2) = (x + 4) ln (x - 2) : x = 3, x = 4

x = 3, x = 4

7^{5 x - 4} = 14

2^{2 x} = n + 1

2^{4 x - 1} = 3^{5 - 2 x}

2^{4 x + 3} = 6

e^{2 x} + 42 = - 13 e^{x}

What is the answer to (x-2)^{x^2-2x}=(x-2)^{x+4} ?
The answer to (x-2)^{x^2-2x}=(x-2)^{x+4} is x=3,x=4
Solve for x: (x-2)^{x^2-2x}=(x-2)^{x+4}
The solution is x=3,x=4