How do I find the value of #log 1000#?

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Oct 5, 2015

The answer is 3.

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:

Logarithmic form and exponential form from moodle2.rockyview.ab.ca.

So therefore we can rewrite the problem as:

#10^? = 1000#

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

Hence, the answer is 3.

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

Hope that helps :)

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Answer:

#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

#"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 " "rarr# because #3^2 = 9#

Can you explain why the following are true?

#log_5 25 = 2color(white)(xxxx)log_4 64 = 3color(white)(xxxx)log_9 81 = 2#

#log_10 10 = 1color(white)(xxxx)log_5 625 = 4color(white)(xxxx)log_10 1 = 0#

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