If 5^(x − 3) × 3^(2x − 8) = 225, then x equals:

5. 225 = 9 × 25 = 3² × 5². Matching bases gives 5^(x − 3) = 5² so x − 3 = 2, and 3^(2x − 8) = 3² so 2x − 8 = 2. Both give x = 5.

If $5^{x - 3} \times 3^{2 x - 8} = 225$ , then $x$ equals:

Competition practiceNumber & Arithmetic

225 =

9 \times 25 = 3^{2} \times 5^{2}

. Matching bases gives

5^{x - 3} = 5^{2}

x - 3 = 2

, and

3^{2 x - 8} = 3^{2}

2 x - 8 = 2

. Both give

x = 5

Answer: C) 5

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