What is the answer to 5^x+5^{x-1}+5^{x-2}=31 ?

The answer to 5^x+5^{x-1}+5^{x-2}=31 is x=2

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5^x+5^{x-1}+5^{x-2}=31

5^{x} + 5^{x - 1} + 5^{x - 2} = 31

x = 2

Solution steps

5^{x} + 5^{x - 1} + 5^{x - 2} = 31

Factor

5^{x} + 5^{x - 1} + 5^{x - 2} : 31 \cdot 5^{x - 2}

31 \cdot 5^{x - 2} = 31

Divide both sides by

31

5^{x - 2} = 1

Apply exponent rules

(x - 2) ln (5) = ln (1)

Solve

(x - 2) ln (5) = ln (1) : x = 2

x = 2

5^{5 x - 4} = (\frac{1}{5})^{x + 1}

100 = 2 e^{\frac{3}{x}}

64 = 4^{2 x - 3}

6 (10)^{x} + (10)^{x - 1} = 2

x, 5^{2 x - 5} = 125

What is the answer to 5^x+5^{x-1}+5^{x-2}=31 ?
The answer to 5^x+5^{x-1}+5^{x-2}=31 is x=2
Solve for x: 5^x+5^{x-1}+5^{x-2}=31
The solution is x=2