Other questions
0

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

0

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

Your answer