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  4. Match the following: If log 2=0.3010 and log 3=0.4771 then find the values of List-I List-II I log 6 P 1.0791 II log 9 Q 0.7781 III log 12 R 0.9542 S 0.8214

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Q. Match the following:
If $\log 2=0.3010$ and $\log 3=0.4771$ then find the values of
List-I List-II
I $\log 6$ P 1.0791
II $\log 9$ Q 0.7781
III $\log 12$ R 0.9542
S 0.8214

Logarithm

Solution:

I. $\log 6 =\log (2 \times 3)=\log 2+\log 3 $
$ =0.3010+0.4771=0.7781$
II. $\log 9 =\log (3)^2=2 \log 3=2(0.4771) $
$ =0.9542$
III. $\log 12 =\log (4 \times 3)=\log \left(2^2 \times 3\right) $
$ =\log 2^2+\log 3=2 \log 2+\log 3$
$ =2(0.3010)+0.4771=1.0791$