Logarithm Calculator
Calculate log base 10, log base e (ln), or log base n for any positive number.
Tip: For log10(x), leave base blank or enter 10.
For ln(x), enter e as the base.
For logn(x), enter your own base.
For ln(x), enter e as the base.
For logn(x), enter your own base.
log
10
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100
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How to Calculate Logarithms
- Base 10 (Common Log): log₁₀(x) is the exponent to which 10 must be raised to get x.
- Base e (Natural Log): ln(x) is the exponent to which e (≈2.718) must be raised to get x.
- Base n: logₙ(x) is the exponent to which n must be raised to get x.
Example: log₁₀(100) = 2, ln(e) = 1, log₂(8) = 3.
How to Build Skills with Logarithms
- Practice with Different Bases: Try calculating logs with base 10, e, 2, and other numbers to see how the results change.
- Understand Logarithm Properties: Learn and use rules like logb(xy) = logb(x) + logb(y) and logb(xk) = k·logb(x).
- Apply to Real-World Problems: Use logarithms for pH in chemistry, decibels in sound, population growth, and compound interest in finance.
- Check with Exponentials: After calculating logb(x), check your answer by raising the base to the result (banswer = x).
- Use Technology: Use calculators, spreadsheets, or programming languages to compute logs for large or complex numbers.
Example: To solve for x in 2x = 16, use log2(16) = 4, because 2⁴ = 16.
Frequently Asked Questions
A logarithm is the exponent to which a base must be raised to produce a given number. For example, log₁₀(100) = 2 because 10² = 100.
To calculate a logarithm, use the formula log_b(a) = x, which means b^x = a. You can use a calculator or logarithm tables.
Logarithms are used in mathematics, science, engineering, and finance for solving exponential equations, measuring sound intensity, pH, and more.