The Log Calculator computes logarithms with any base. It supports natural logarithms (ln, base e), common logarithms (log base 10), binary logarithms (log base 2), and logarithms with any custom base.
Enter a number and choose your base to get the logarithm instantly. The calculator also shows the relationship between the logarithm and its equivalent exponential form.
Your calculations will appear here
A logarithm answers the question: "To what power must the base be raised to produce a given number?" If b^x = y, then log_b(y) = x. Logarithms are the inverse operation of exponentiation.
The three most common logarithms are: the natural logarithm (ln, base e = 2.718...) used in calculus and science, the common logarithm (log, base 10) used in engineering and everyday calculations, and the binary logarithm (log base 2) used in computer science.
Problem: Find log base 10 of 1000
Solution: 10^? = 1000, so 10^3 = 1000
Answer: log(1000) = 3
Problem: Find ln(e^5)
Solution: ln(e^5) = 5 * ln(e) = 5 * 1
Answer: ln(e^5) = 5
Problem: Find log base 2 of 64
Solution: 2^? = 64, so 2^6 = 64
Answer: log2(64) = 6
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