Question

Expand log 77/25
This is in a 10class

Answer 1

Answer:

$\log(\frac{77}{25})]=\log\:7+\log\:11-2\:\log\:5$

Step-by-step explanation:

$\log(\frac{77}{25})$

using, Quotient rule of logarithm

$\boxed{\log(\frac{M}{N})=\log\:M-\log\:N}$

$=\log\:77-\log\:25$

$=\log\:(7\times\:11)-\log\:(5\times\:5)$

using, product rule of logaarithm

$\boxed{\log(MN)=\log\:M+\log\:N}$

$=\log\:7+\log\:11-(\log\:5+\log\:5)$

$=\log\:7+\log\:11-2\:\log\:5$

$\implies\boxed{\log(\frac{77}{25})]=\log\:7+\log\:11-2\:\log\:5}$