Question

1/2log5 36+2log5 7 -1/2log5 12

Answer 1

Given,

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

We know x log y = log y^x . This is called power law.

Using this :-

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

$log_{5}(6)+log_{5}(49)-log_{5}(2 \sqrt{3} )$

We know log m + log n = log mn. This is called product law.

Using this law, we get :-

$log_{5}(6 \times 49)-log_{5}(2 \sqrt{3} )$

We know , log m - log n = log m/n . This is called quotient law.

Using this law, we get :-

$log_{5}( \frac{6\times 49}{2\times\sqrt{3} } )$

$log_{5}( \frac{3 \times 49}{ \sqrt{3} } )$

$log_{5}( \sqrt{3} \times 49 )$

$log_{5}(49 \sqrt{3} )$

Answer = log 49√3 to the base 5.