Logarithm Calculator
How It Works
This logarithm calculator uses established formulas to provide accurate results.
The basic rule:
- log_b(x) = y means b^y = x
- Change of base: log_b(x) = ln(x) / ln(b)
- ln(x) = log_e(x)
- log₁₀(x) = log(x)
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is a logarithm?
A logarithm answers the question: what exponent must I raise the base to in order to get this value? log_b(x) = y means b^y = x. For example, log_2(8) = 3 because 2³ = 8.
What is the change of base formula?
To calculate a logarithm with any base using a calculator that only has ln or log₁₀: log_b(x) = ln(x)/ln(b) = log₁₀(x)/log₁₀(b). This works for any base b > 0, b ≠ 1.
What is the difference between ln and log?
ln is the natural logarithm (base e ≈ 2.71828), used extensively in calculus and science. log (or log₁₀) is the common logarithm (base 10), common in chemistry and engineering. In pure math, log sometimes means ln.
Why can't the base be 1 or the value be 0 or negative?
Base 1 would make every logarithm undefined (1 raised to any power is always 1). Logarithms of zero or negative numbers are undefined in real numbers because no real exponent can make a positive base produce zero or a negative result.