How do you evaluate $\log 10,000$?
Answer
627.6k+ views
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 $.
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 $.
Recently Updated Pages
Write any three differences between metals and nonmetals class 10 social science CBSE

Amit standing on a horizontal plane finds a bird flying class 10 maths CBSE

Two circles of radii 5 cm and 3 cm intersect at two class 10 maths CBSE

Solve the following i John and Jivanti together have class 10 maths CBSE

What is the relation between orthocenter circumcentre class 10 maths CBSE

Two plane mirrors are inclined at 70circ A ray incident class 10 physics CBSE

Trending doubts
Explain the Treaty of Vienna of 1815 class 10 social science CBSE

Which country is known as "The land of Fire and Ice"?

1 GB equals how many MB?

10 examples of evaporation in daily life with explanations

What is the full form of POSCO class 10 social science CBSE

Make a sketch of the human nerve cell What function class 10 biology CBSE

