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Sum of Logarithms

Prove the following:

$\log_a(xy) = log_ax\;+\;log_ay$

edited Jun 21 '19 at 15:29 Asked Jun 21 '19 at 14:28 by Lucy

1 Answer

$Let\; m=\log_ax \;and\; n=\;log_ay\\[10pt] p=log_a(xy) \leftrightarrow xy=a^p \\[10pt] xy=a^ma^n =a^{m+n}\\[10pt] Let\; k= m+n\\[10pt] log_a(xy)=m+n = log_ax +log_ay$

asked Jun 21 '19 at 15:28 by Lucy

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Sum of Logarithms

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