What is the answer to 5^{x+2}-5^x+5^{x-1}=121 ?

The answer to 5^{x+2}-5^x+5^{x-1}=121 is x=1

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5^{x+2}-5^x+5^{x-1}=121

5^{x + 2} - 5^{x} + 5^{x - 1} = 121

x = 1

Solution steps

5^{x + 2} - 5^{x} + 5^{x - 1} = 121

Factor

5^{x + 2} - 5^{x} + 5^{x - 1} : 121 \cdot 5^{x - 1}

121 \cdot 5^{x - 1} = 121

Divide both sides by

121

5^{x - 1} = 1

Apply exponent rules

(x - 1) ln (5) = ln (1)

Solve

(x - 1) ln (5) = ln (1) : x = 1

x = 1

3 \times 2^{2 x} - 10 (2)^{x} = 0

1 6^{3 x - 3} = 6 4^{x + 3}

2^{2 + x} - 2^{2 - x} = 15

2^{3 - 2 x} = 8

3^{x^{2}} = 9^{x + 4}

What is the answer to 5^{x+2}-5^x+5^{x-1}=121 ?
The answer to 5^{x+2}-5^x+5^{x-1}=121 is x=1
Solve for x: 5^{x+2}-5^x+5^{x-1}=121
The solution is x=1