What is the answer to 5^{x+1}+5^{x-2}+5^{x-1}=131 ?

The answer to 5^{x+1}+5^{x-2}+5^{x-1}=131 is x=2

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5^{x+1}+5^{x-2}+5^{x-1}=131

5^{x + 1} + 5^{x - 2} + 5^{x - 1} = 131

x = 2

Solution steps

5^{x + 1} + 5^{x - 2} + 5^{x - 1} = 131

Factor

5^{x + 1} + 5^{x - 2} + 5^{x - 1} : 131 \cdot 5^{x - 2}

131 \cdot 5^{x - 2} = 131

Divide both sides by

131

5^{x - 2} = 1

Apply exponent rules

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

Solve

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

x = 2

4^{3 x + 5} = 6 4^{x} \cdot 4^{5}

b^{y} = c

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

8 = 4^{x - 2}

y, x^{y} = y^{x}

What is the answer to 5^{x+1}+5^{x-2}+5^{x-1}=131 ?
The answer to 5^{x+1}+5^{x-2}+5^{x-1}=131 is x=2
Solve for x: 5^{x+1}+5^{x-2}+5^{x-1}=131
The solution is x=2