Question

( log 25/16 + log 4/5)/log 5/4

Answer 1

Step-by-step explanation:

log(25/16×4/5)/log5/4

=log(5/4)/log5/4

=1

Answer 2

Given:

Consider the given expression

$\frac{(log\frac{25}{16}+log\frac{4}{5}) }{log\frac{5}{4} }$

Find:

We need to simplyfy this expression

Solution:

We have logirthmic property

$logm+logn = logmn\\\\log\frac{m}{n}=logm - logn$

using the fact we have

$\frac{(log\frac{25}{16}+log\frac{4}{5}) }{log\frac{5}{4} }$

$\frac{log(\frac{25}{16}.\frac{4}{5})}{log\frac{5}{4}}=\frac{log\frac{5}{4}}{log\frac{5}{4}}=1$