If 125\(_x\) = 20\(_{10}\) find x

Explanation

125\(_x\) = 20\(_{10}\)
1 x X\(^2\) + 2 x X\(^1\) + 5x X \(^0\) = 20
X2 + 2X + 5 = 20
X\(^2\) + 2X - 15 = 0
(X + 5)( X - 3) = 0
X + 5 implies X = -5
X - 3 implies X = 3
But X cannot be negative
∴X = 3

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