SOLUTION: If log5=a and log4=b, express the logarithm in terms of a and b. log 0.16

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Question 1018450: If log5=a and log4=b, express the logarithm in terms of a and b. log 0.16
Answer by ikleyn(52817) About Me  (Show Source):
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If log5=a and log4=b, express the logarithm in terms of a and b. log 0.16
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Notice that 0.16 = 16%2F100 = 4%5E2%2F%284%2A5%5E2%29 = 4%2F5%5E2.

Therefore, log%2810%2C+%280.16%29%29 = log%2810%2C+%284%2F5%5E2%29%29 = log%2810%2C4%29+-+2%2Alog%2810%2C5%29 = b - 2a.