Logarithm Calculator
Compute logarithms in any base, including natural log (ln) and common log (log10).
Calculate Logarithms
log₁₀(100) = 0
ln(x) = 0
log₁₀(x) = 0
About this Calculator
Compute logarithms in any base, including natural log (ln) and common log (log10).
Formula & Calculations
Formula
log_b(x) = ln(x) / ln(b), ln(x) = natural log, log10(x) = common logWhere:
- x=The value whose logarithm is being computed (must be positive)
- b=The base of the logarithm (must be positive and not equal to 1)
- log_b(x)=The exponent to which b must be raised to obtain x
Assumptions
- The value x must be strictly positive (x > 0). Logarithms of zero or negative numbers are undefined in real numbers.
- The base must be positive and not equal to 1.
Calculation Examples
Example 1
Inputs:Value: 100, Base: 10
Result:log10(100) = 2
10 must be raised to the power of 2 to equal 100 (10^2 = 100).
Example 2
Inputs:Value: 8, Base: 2
Result:log2(8) = 3
2^3 = 8, so the logarithm base 2 of 8 is 3.
Frequently Asked Questions
What is a natural logarithm (ln)?
The natural logarithm uses Euler's number e (approximately 2.71828) as its base. It is widely used in calculus, compound growth problems, and scientific calculations.
Why can't I take the logarithm of zero or a negative number?
In the real number system, there is no exponent you can raise a positive base to that results in zero or a negative number. Logarithms of non-positive values are only defined in the complex number system.