What is the answer to (5^{x-2})^{x-3}=1 ?

The answer to (5^{x-2})^{x-3}=1 is x=3,x=2

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(5^{x-2})^{x-3}=1

(5^{x - 2})^{x - 3} = 1

x = 3, x = 2

Solution steps

(5^{x - 2})^{x - 3} = 1

Apply exponent rules

(x - 3) ln (5^{x - 2}) = ln (1)

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or ln (5^{x - 2}) = 0

Solve

x - 3 = 0 : x = 3

Solve

ln (5^{x - 2}) = 0 : x = 2

x = 3, x = 2

e^{2 x} x = 2

4^{x} - 8 \times 2^{x} = 2^{x - 2} - 2

5^{3 x + 2} = 2 5^{x - 8}

2 7^{2 x - 3} = 27

5^{- x} = 15

What is the answer to (5^{x-2})^{x-3}=1 ?
The answer to (5^{x-2})^{x-3}=1 is x=3,x=2
Solve for x: (5^{x-2})^{x-3}=1
The solution is x=3,x=2