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$5^{(x+2)} = 125$

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Find the missing exponent or base

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Q.

5^{(x+2)} = 125

Recognize Power of $5$ : Recognize that $125$ is a power of $5$ . $125$ can be written as $5^3$ because $5 \times 5 \times 5 = 125$ .
Set Exponents Equal: Set the exponents equal to each other since the bases are the same. $\newline$ Since $5^{x+2} = 5^3$ , we can set $x + 2 = 3$ because if the bases are the same, the exponents must be equal for the two expressions to be equal.
Solve for x: Solve for x. $\newline$ Subtract $2$ from both sides of the equation $x + 2 = 3$ to isolate $x$ . $\newline$ $x + 2 - 2 = 3 - 2$ $\newline$ $x = 1$

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