Question

How do you evaluate $\log 10,000$?

Answer 1

Hint:
It is always better to look at questions and verify, is it $\ln $ or $\log $ ? because $\ln $ is $e$ base function and $\log $is 10 base function. Here we have $\log $ so base is 10.

Complete step by step answer:
To solve this question you must know this questions:
${\log _a}a = 1$
$\log {a^b} = b\log a$
As we know 10,000 can be written as ${10^4}$ .
So here, $\log 10,000$ can be written as $\log {10^4}$
From the equations (1.2) we get,
$\log {10^4} = 4\log 10$
Now log is 10 base function so,
From equation (1.1) we get,
$4{\log _{10}}10 = 4(1) = 4$

So, after evaluating $\log 10,000$ we get 4.

Note:
As you can see if you know basic $\log $ formulas then these types of questions are very easy to solve. You must remember the difference between $\ln $ and $\log $. $\ln $ is an e base function. $\log $ is 10 base functions. And the same formulas apply for $\ln $.