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If \(a = \log_{10} 3\) and \(b = \log_{10} 7\), then find \(\log_7 9\) in terms of a and b.

Guest Dec 16, 2019

CPhill · Answer 1 · 2019-12-16T01:36:22

a = log₁₀ 3

b = log₁₀ 7

By the change- of- base theorem we have that

a = log 3 / log 10 = log 3

b = log 7 / log 10 = log 7 [Note that log 10 = 1 ]

Also note that

2a = 2 log₁₀3 = log₁₀3^2 = log₁₀ 9 = log 9 / log 10 = log 9

So

log₇ 9 = log 9 / log 7 = 2a / b