Logarithm Calculator
\(\displaystyle \large{\log_a{b}} \)
\(\displaystyle \left(a,b\gt0,a\neq1\right) \)
How to Use
- Positive integer, decimal, and fraction can be entered for \(a\) and \(b\).
- 1 cannot be entered for \(a\).
- Napier number \(e\) can also be entered for \(a\).
- Enter fraction as 1/2, 3/5, etc.
What is logarithm?
Logarithm is a calculation that is the inverse of exponent.
For example, suppose we have the following exponential expression.
\[ b=a^{x} \]
This expression can be expressed using logarithms as follows
\[ x=\log_{a}{b} \]
The domain of a is as follows
\[ a\gt0,a\neq1 \]
The domain of b is as follows
\[ b\gt0 \]
Example
Example 1
Calculate \( \log_{3}{27} \).
Solution
\[ \log_{3}{27}=3 \]
Example 2
Calculate \(\displaystyle \log_{2}{ \frac{1}{16} } \).
Solution
\[ \log_{2}{\frac{1}{16}}=-4 \]