Logarithm Input
Calculate the logarithm of a number with any base.
Equation
Reference
The logarithm of a number x is the exponent to which the base b must be raised to produce x.
- Common Log (log): Base 10
- Natural Log (ln): Base e (≈ 2.718)
- Binary Log (lb): Base 2
Logarithm Guide Guide
How to Use
- 1Enter the number (x) you want to calculate the logarithm for.
- 2Enter the base (b). Common bases are 10 (common log) and e (natural log).
- 3Click calculate to find the exponent y.
Formula & Logic
A logarithm tells you what exponent needed to raise a base to in order to get a specific number. It is the inverse operation of exponentiation.
Practical Applications
Sound Intensity
Decibels (dB) are calculated using logarithms to represent the vast range of human hearing sensitivity.
Earthquakes
The Richter scale uses base-10 logarithms; an earthquake of magnitude 6 is 10 times stronger than magnitude 5.
Information Theory
Calculate entropy and the amount of information (bits) contained in a message.
Frequently Asked Questions
Q.What is the Natural Logarithm (ln)?
The natural logarithm uses the mathematical constant e (approx. 2.718) as its base. It is written as ln(x) instead of log_e(x).
Q.Why can't I take the log of a negative number?
For real numbers, you cannot raise a positive base to any power and get a negative result. Therefore, the domain of the logarithm function is only positive numbers (x > 0).
Q.What is Log Base 10?
Log base 10 is called the 'common logarithm'. It is widely used in science and engineering. If you see 'log(x)' without a base written, it usually implies base 10.