Question

Find the value of log (2000) if log 2 = 0.3010​

Answer 1

Answer:

If log 2 = 0.3010

Then ,

log of 2000 = 3.3010

Answer 2

Answer:

3.3010

Step-by-step explanation:

$log(2000) = log(2 \times {10}^{3} )$

But in log multiplication can be done as addition.

So,

$log(2 \times {10}^{3} ) = log(2) + log(10^{3})$

Now power can be kept further so,

$log( {10}^{3} ) = 3 log(10)$

But,

$log(10) = 1$

So,

$log( {10}^{3} ) = 3 \times 1 = 3$

and,

$log(2) = 0.3010$

So,

$log(2) + log( {10}^{3} ) = 0.3010 + 3 = 3.3010$

Hence,

log(2000)=3.3010