Digital ACT Math Practice Question #1233
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Decompose $45\sqrt{b} = 3^2 \cdot 5^1 \cdot b^{1/2} \implies 2x + 1y + 1/2$.
Notice $45 = 9 \times 5 = 3^2 \times 5$. Using log product and power rules: $$\log_b(45\sqrt{b}) = \log_b(3^2 \cdot 5 \cdot b^{1/2}) = \log_b(3^2) + \log_b(5) + \log_b(b^{1/2})$$ $$= 2\log_b(3) + \log_b(5) + \frac{1}{2}\log_b(b) = 2x + y + ...
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