Question

Simplify log5 s + log5 11 – log5 15 – log5 t

Answer 1

\[\log_{b} a= \log a/\log b\]

Answer 2

\[log_{5} s + log_{5} 11 - log_{5} 15 -log_{5} t\]
we know that
\[log_a(x)+log_a(y)=log_a(xy)\]
and
\[log_a(x)-log_a(y)=log_a(x/y)\]
so using the above two properties
\[log_5 s*11-(log_5 15+log_5 t)\]
using the addition property for the terms in bracket
we get
\[log_5s*11-log_5 15*t\]
now using the subtraction property
we obtain
\[log_5 \frac{11*s}{15*t}\]