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Question
Answer the following:
If a2 = b3 = c4 = d5, show that loga bcd = `47/30`
Solution
a2 = b3 = c4 = d5
Taking log to the base a throughout, we get
loga a2 = loga b3 = loga c4 = loga d5
∴ 2 loga a = 3 loga b = 4 loga c = 5 loga d
∴ 2(1) = 3 loga b = 4 loga c = 5 loga d
∴ loga b = `2/3`, loga c = `2/4 = 1/2` and loga d = `2/5`
∴ loga b + loga c + loga d = `2/3 + 1/2 + 2/5`
∴ loga bcd = `47/30`
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