Frequently Asked Questions
What does log mean?
log_b(x) answers "what power do I raise b to in order to get x?" So log₁₀(1000) = 3 because 10³ = 1000. It is the inverse of exponentiation.
When do I use natural log (ln) vs log base 10?
Use ln in continuous growth, calculus, and most physics/biology. Use log₁₀ in pH, decibels, and the Richter scale. Computer science often uses log₂.
How do I change bases?
log_b(x) = log(x) / log(b) using any base. So log₂(32) = log(32)/log(2) = 5. This lets a calculator with only ln or log₁₀ compute any base.
Why can't I take the log of zero or a negative number?
No real exponent of a positive base produces 0 or a negative result. log(0) approaches negative infinity, and log of negatives gives complex numbers.
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