Question

expand log 385 at the base 10

Answer 1

Logarithms to the base 10 are called common Logarithms.

We use few formulae to simplify this.

385 can be written as product of three numbers, 5, 11 & 7.

So, log ( 385) = log ( 5 * 7 * 11)

Using the formula, loga + log b = log ab

This simplifies to,

log (385) = log 5 + log 7 + log 11

Substitute the values of log 5, log 7, log 11 gives the value of log385.

$log_{10}(385 ) \\ = log_{10}(5 \times 11 \times 7) \\ = log_{10}(5) + log_{10}(7) + log_{10}(11) \\ = 0.698 + 0.845 + 1.041 = 2.585$

Expansion of $log_{10}(385 ) = log_{10}(5) + log_{10}(7) + log_{10}(11)$

Answer 2

Answer:

Expansion $log_{10}(385 )= log_{10}(5) + log_{10}(7) + log_{10}(11)$

Solution - 2.585

Step-by-step explanation:

To expand : log 385 at the base 10 i.e, $log_{10}(385 )$

Solution :

First we factor the 385,

$385=5\times7\times11$

Now,

$log_{10}(385)= log_{10}(5 \times 11 \times 7)$

By property of logarithmic,

$log(A\times B)=logA+logB$

$log_{10}(5 \times 11 \times 7)= log_{10}(5) + log_{10}(7) + log_{10}(11)$

This is the expansion of the given expression.

Now, we do the solution:

$log_{10}(5)+log_{10}(7)+log_{10}(11)=0.698+0.845+1.041=2.585$

Therefore,The solution is 2.585 and expansion is

$log_{10}(385 )= log_{10}(5) + log_{10}(7) + log_{10}(11)$