This kind of math puzzles is an educational activity for practicing children’s math skills. It’s also helpful for adults to have fun and challenge their brains!

## Challenge:

If \(5^x + 5^{x+1} + 5^{x+2}=\frac{31}{25}\), what is the value of x?

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The correct answer is \(-2\).

Solve for x:

\(5^x + 5^{x+1} + 5^{x+2}=\frac{31}{25}\)

The common factor is \(5^x\). Then,

\(5^x(1+5^1+5^2)=\frac{31}{25}⇒5^x(31)=\frac{31}{25}⇒5^x=\frac{\frac{31}{25}}{31}⇒\)

\(5^x=\frac{31}{25}÷\frac{31}{1}=\frac{31}{25}×\frac{1}{31}=\frac{1}{25}\)

\(\frac{1}{25}=5^{-2}\) Then: \(5^x=5^{-2}⇒ x = -2\)