Question

Show that log√7 + log√20 - log√14 = 1/2

Answer 1

Alright, lets get started.

$log \sqrt{7} + log \sqrt{20} - log\sqrt{14} = \frac{1}{2}$

We could write this square root as $\frac{1}{2}$

$log7^{\frac{1}{2}} + log20^{\frac{1}{2}}- log14^{\frac{1}{2}}$

Using the property of $logm^{n } = n log (m)$

$\frac{1}{2}log 7 + \frac{1}{2} log 20 - \frac{1}{2} log14$

$\frac{1}{2}$ is common in each term, so

$\frac{1}{2}(log7 + log 20 - log 14)$

Using property of $log m + log n = log(mn)$

$\frac{1}{2}(log 140 - log 14)$

Using property of $log m - log n = log\frac{m}{n}$

$\frac{1}{2}log\frac{140}{14}$

$\frac{1}{2} log 10$

log 10 value is 1 , hence

$\frac{1}{2} * 1 = \frac{1}{2}$ : Answer

Hope it will help :)