Given that $\log_a 125 - 3\log_a \sqrt{b} + \log_a c = 3$, express $a$ in terms of $b$ an

Question

Given that $\log_a 125 - 3\log_a \sqrt{b} + \log_a c = 3$, express $a$ in terms of $b$ and $c$.[3] Show that $5^{n + 1} - 4(5^n) + 5^{n - 1}$ is divisible by $2$ for all positive integers of $n$.[3]

Accepted Answer

(a) $a = \frac{5 \sqrt[3]{c} }{\sqrt{b}}$ (b) $ \dots = 6(5^{n-1})$ Since it has a factor of $6$ it is divisible by $2$

2024 GESS PRELIMS P1 Q13

2024 GESS PRELIMS P1 Q13

Solution:

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