What is the answer to 5^{x-2}-5^x+5^{x+1}=505 ?

The answer to 5^{x-2}-5^x+5^{x+1}=505 is x=3

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5^{x-2}-5^x+5^{x+1}=505

5^{x - 2} - 5^{x} + 5^{x + 1} = 505

x = 3

Solution steps

5^{x - 2} - 5^{x} + 5^{x + 1} = 505

Factor

5^{x - 2} - 5^{x} + 5^{x + 1} : 101 \cdot 5^{x - 2}

101 \cdot 5^{x - 2} = 505

Divide both sides by

101

5^{x - 2} = 5

Apply exponent rules

x - 2 = 1

Solve

x - 2 = 1 : x = 3

x = 3

4^{\frac{2 z}{3}} = 8^{(z + 2)}

9^{x} = 3

8 1^{3^{2 x}} = 2 7^{4^{2 x}}

9^{2 x} = 27

2^{2 x - 1} - 6 \cdot 2^{x - 1} + 4 = 0

What is the answer to 5^{x-2}-5^x+5^{x+1}=505 ?
The answer to 5^{x-2}-5^x+5^{x+1}=505 is x=3
Solve for x: 5^{x-2}-5^x+5^{x+1}=505
The solution is x=3