Question

Simplify:
$\frac{1}{2} \log_{5} 36 + 2\log_{5} 7 - \frac{1}{2} \log_{5} 12$

Answer 1

Please see the attachment

Answer 2

Answer:

$\frac{1}{2}log_{5}36+2log_{5}7-\frac{1}{2}log_{5}12=log_{5}\frac{294}{\sqrt{12}}$

Step-by-step explanation:

From the given question,

We have been provided that,

$\frac{1}{2}log_{5}36+2log_{5}7-\frac{1}{2}log_{5}12$

Now,

We have to find the solution by the simplification of the equation,

Using the properties of logarithms we get that,

$alogb=logb^{a}\\and,\\loga+logb=logab\\loga-logb=log\frac{a}{b}$

Therefore, using the same properties we get,

$\frac{1}{2}log_{5}36+2log_{5}7-\frac{1}{2}log_{5}12=log_{5}(36)^{\frac{1}{2}}+log_{5}(7)^{2}-log_{5}\sqrt{12}\\=log_{5}6+log_{5}49-log_{5}\sqrt{12}\\=log_{5}\frac{294}{\sqrt{12}}$

Therefore,

On solving the equation using the properties of the logarithms stated above we get our simplified solution as,

$log_{5}\frac{294}{\sqrt{12}}$