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Log Calculator
Find the value of the log by entering the base and log value in the log base calculator.
Table of Contents:
This logarithmic calculator can compute the value of the log for any base within a matter of seconds. Through this log calculator, users can find long for any base including 10, e (ln), and 2.
What is log?
The concept of the log is related to exponents to a great extent. According to Khan Academy:
“Logarithms are another way of thinking about exponents.”
A logarithm is used to find the number which, if raised as a power to the base of the log, will calculate a certain value (log value).
log_{b}c =b^{c}a
Did you know? The shell of the nautilus is a perfect example of a logarithmic spiral. Logs can be reversed with anitlog. You can use antilog calculator to find the antilog of a given value.
Log Rules
There are certain rules of log that make calculations easy.
Product rule
If two values to be multiplied have the same log base, the answer will be equal to the sum of the individual log.
log_{b}(CD) = log_{b}(C) + log_{b}(D)
Quotient Rule
Similarly, two values in the division with the same log base will be equal to the difference of the individual log.
log_{b}(C/D) = log_{b}C - log_{b}D
Power Rule
If the value of the log is raised to some power then that power will be multiplied with the log of value.
log_{b}(x^{y}) = y * log_{b}(x)
Log base switch Rule
The base can be replaced with log value in a reciprocal of log equation.
log_{b}(x) =1 / log_{x}(b)
Change of base Rule
To introduce a new base in the log equation following changes are made.
log_{b}(x) = log_{c}(x) / log_{c}(b)
Daily life use of log
Some examples of the use of logarithm in daily life are:
- Sound energy (calculating decibels)
- pH of Chemicals
- Environmental sciences
Log | Value |
Log 0 | Undefined |
Log of 3 | 0.47712 |
Log of 3 base 4 | 0.7924 |
Log of 3 base 27 | 0.3333 |
Log of 3 base 2 | 1.5849 |
Log of 3/5 | -0.2218 |
Log of 3 base 5 | 0.6826 |
Log of 2 | 0.3010 |
Log of 2 base 8 | 0.3333 |
Log of 2 base 4 | 0.5 |
Log of 2 to the base 10 | 0.3010 |
Log of 100 | 2 |
Log of 1/2 | -0.3010 |
Log of 1 million | 6 |
Log of 1.5 | 0.1760 |
Log 2(3) | 0.9030 |
Value of log 5 | 0.6989 |
Log of e | 0.4342 |
Log of infinity | ∞ |
Log base 2 of 8 | 0.3333 |
Log_{2}(128) | 7 |
Log_{2}(105) | 6.7142 |
Log_{2}(100) | 6.6438 |