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5 March, 03:13

Prove that 1:loga ab + 1:logb ab=1

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  1. 5 March, 03:22
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    See below.

    Step-by-step explanation:

    1 : loga ab + 1 : logb ab

    = 1 / (loga ab) + 1 / (loga ab / loga b) { change of log base)

    = 1 / (loga ab) + loga b / (loga ab)

    = (1 + loga b) / loga ab

    = (1 + loga b) / (loga a + loga b) Now loga a = 1 so we have:

    ((1 + loga b) / (1 + loga b)

    = 1.
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