Alright, lets get started.
[tex] log \sqrt{7} + log \sqrt{20} - log\sqrt{14} = \frac{1}{2} [/tex]
We could write this square root as [tex] \frac{1}{2} [/tex]
[tex] log7^{\frac{1}{2}} + log20^{\frac{1}{2}}- log14^{\frac{1}{2}} [/tex]
Using the property of [tex] logm^{n } = n log (m) [/tex]
[tex] \frac{1}{2}log 7 + \frac{1}{2} log 20 - \frac{1}{2} log14 [/tex]
[tex] \frac{1}{2} [/tex] is common in each term, so
[tex] \frac{1}{2}(log7 + log 20 - log 14) [/tex]
Using property of [tex] log m + log n = log(mn) [/tex]
[tex] \frac{1}{2}(log 140 - log 14) [/tex]
Using property of [tex] log m - log n = log\frac{m}{n} [/tex]
[tex] \frac{1}{2}log\frac{140}{14} [/tex]
[tex] \frac{1}{2} log 10
[/tex]
log 10 value is 1 , hence
[tex] \frac{1}{2} * 1 = \frac{1}{2} [/tex] : Answer
Hope it will help :)
