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CEMC Cayley, 2021 Difficulty 1.6 Junior Find the answer Canada
If 3 x = 5 3^{x}=5 3 x = 5 3 x + 2 3^{x+2} 3 x + 2
Pick one
A 10 10 10 B 25 25 25 C 2187 2187 2187 D 14 14 14 E 45 45 45
Solution Using exponent laws, 3 x + 2 = 3 x ⋅ 3 2 = 3 x ⋅ 9 3^{x+2} = 3^x \cdot 3^2 = 3^x \cdot 9 3 x + 2 = 3 x ⋅ 3 2 = 3 x ⋅ 9
Since 3 x = 5 3^x=5 3 x = 5 3 x + 2 = 3 x ⋅ 9 = 5 ⋅ 9 = 45 3^{x+2} = 3^x \cdot 9 = 5 \cdot 9 = 45 3 x + 2 = 3 x ⋅ 9 = 5 ⋅ 9 = 45
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