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[Step 13: Common Logarithms (1): The World of Base 10 (The World of Decimal System)] Learning Logarithms in 1 Minute: A 20-Part Series to Master Overwhelming Knowledge

2026年4月10日 12:36

Hello, this is KoTa.

Up until now, various bases like '2' or '3' have appeared, but the numbers we use in our daily lives increase in digits as '10, 100, 1000...', which is the decimal system.

Therefore, **'logarithms with base 10' are specially called 'common logarithms'** and are the most frequently used.

log_10 M

This 'base 10' is so obvious that it is sometimes omitted and written simply as log M.

The amazing thing about common logarithms is that you can tell 'roughly how large' a number is just by looking at it.

log_10 10 = 1
log_10 100 = 2
log_10 1000 = 3

In other words, the answer to a common logarithm (1, 2, 3...) almost matches the 'number of zeros (number of digits)' of that number. If you know 'the log of this number is about 5.3', you can intuitively understand that 'oh, it's a large number with about 5 zeros (in the hundred-thousands place)'.

Key points for this lesson

Logarithms with base 10 are called common logarithms.
Since we use the 'decimal system', base 10 is very compatible.
The value of a common logarithm tells you the '**scale (magnitude of digits)**' of that number.

What is the next step?

Step 14: Common Logarithms (2): Instantly Guessing 'How Many Digits' a Huge Number Has

The number '2 to the power of 100' would fill up a notebook if you calculated it out. However, by using common logarithms, you can accurately determine 'how many digits this number has' with just a few lines of calculation. Let's learn this magical digit-counting technique!

See you then!