# How do I find the value of log 1000?

Sep 13, 2014

You can do this in 2 different ways.

One is to just plug it in your calculator, and the other is by hand.

By hand, you need to know that $\log$ is the same thing as ${\log}_{10}$.

Therefore, if you rewrite the problem as such, you get:

${\log}_{10} 1000$ = ?

From here, it would be a lot easier to solve this problem by converting the logarithm into exponential form (which is simply something with an exponent, like ${5}^{2}$)

To understand how to do this, refer to the image below:

So therefore we can rewrite the problem as:

10^? = 1000

And if you know your exponents right, you'll know that ${10}^{3} = 1000$

To know more about how logarithms work, please refer to my explanation in this other answer I contributed to.

Hope that helps :)

Sep 9, 2016

${\log}_{10} 1000 = 3$

#### Explanation:

Think of an expression given in log form as asking a question.
Logs are very closely linked to indices (powers).

(If no base is given, it is always 10.)

In ${\log}_{10} 1000$ The question being asked is..

"What index (power) of 10 " will make " 1000?"

OR

$\text{How can I make " 10 " into " 1000 " using an index (power)?}$

You should know that our number system is based on.

${10}^{1} = 10$
${10}^{2} = 100$
${10}^{3} = 1 , 000$ and so on.

So we can say that "10 raised to the power of 3 is 1000"

Using this to answer the log question gives:

${\log}_{10} 1000 = 3$

In the same way: ${\log}_{3} 9 = 2 \text{ } \rightarrow$ because ${3}^{2} = 9$

Can you explain why the following are true?

${\log}_{5} 25 = 2 \textcolor{w h i t e}{\times \times} {\log}_{4} 64 = 3 \textcolor{w h i t e}{\times \times} {\log}_{9} 81 = 2$

${\log}_{10} 10 = 1 \textcolor{w h i t e}{\times \times} {\log}_{5} 625 = 4 \textcolor{w h i t e}{\times \times} {\log}_{10} 1 = 0$