A logarithm is the inverse of exponentiation. log_b(x) answers the question: what power of b gives x?

What is the difference between log and ln?

log (or log₁₀) uses base 10 and is common in science and engineering. ln uses base e (≈2.718) and is the natural logarithm used in calculus.

Can you take the log of a negative number?

Not in the real number system. Logarithms are only defined for positive real numbers. The complex logarithm extends this to negative numbers.

Logarithm Calculator

Calculate logarithms in any base. Shows natural log (ln), common log (log10), and custom base.

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Number

Custom Base

Log10 Val

2.000000

Ln Val4.605170

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How Logarithms Work

Definition

log_b(x) = y means b^y = x

The logarithm answers: "To what power must I raise the base to get this number?"

Common Types

log₁₀(x): Common logarithm (base 10)

ln(x): Natural logarithm (base e ≈ 2.71828)

log₂(x): Binary logarithm (base 2)

Change of Base Formula

log_b(x) = ln(x) / ln(b)

Example Calculation

Calculate the logarithms of 100.

01log₁₀(100) = 2 (because 10² = 100)
02ln(100) ≈ 4.605170
03log₂(100) = ln(100)/ln(2) ≈ 6.643856

Frequently Asked Questions

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Logarithm Calculator

How Logarithms Work

Definition

Common Types

Change of Base Formula

Example Calculation

Frequently Asked Questions

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