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Log Calculator

Calculate logarithms for Base 10, Natural Log (e), or any custom base.

Enter the number you want to find the log for.
Logarithm Base
Base 10 (Common Log)
Natural (e)
Custom Base
Enter the base value (must be > 0 and not 1).
Result
0.0000
log10(x)
Formula used will appear here.

Antilog (Inverse)

0.0000

Scientific Notation

0e+0

Understanding Logarithms

A logarithm is the power to which a number must be raised in order to get another number. For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:

log10(100) = 2 because 102 = 100

Common Logarithm (Base 10)

This is the logarithm to the base 10. It is widely used in science and engineering, particularly when dealing with the decimal system. You will often see this written simply as log(x).

Natural Logarithm (Base e)

The natural logarithm has the number e (approximately 2.71828) as its base. It is commonly used in physics, chemistry, and mathematics. It is written as ln(x).

Change of Base Formula

Calculators usually only have buttons for log10 and ln. To calculate a logarithm with a different base (like log2), we use the Change of Base Formula:

logb(x) = ln(x) / ln(b)

Antilog Calculator

The antilog (inverse logarithm) is the inverse operation of the logarithm. It raises the base to the power of the logarithm value. If y = logb(x), then x = by. Our calculator displays this automatically for you.

Please enter a valid number.