Logarithms
A logarithm is the inverse of exponentiation, telling us what power a base must be raised to in order to get a given number.
Core concept
If a^x = N, then log base a of N equals x, written as log_a(N) = x, showing the relationship between exponents and logarithms.
How it works
Common logarithms use base 10, written as log(N), while natural logarithms use base e (approximately 2.718), written as ln(N).
Why it matters
Laws of logarithms include: log(mn) = log(m) + log(n), log(m/n) = log(m) - log(n), and log(m^n) = n×log(m).
Key detail
Logarithms are useful for solving exponential equations and are used in fields like science, engineering, and finance.
Exam highlight
Key diagram

Keywords worth remembering
Trending
Most searched
Quick revision
Study resources
Notes & downloads
Quick notes
• If a^x=N, then log_a(N)=x.
• This shows the exponent-logarithm relationship.
• Common logarithms use base 10.
• Natural logarithms use base e (≈2.718).
• log(mn) = log(m) + log(n).
• log(m/n) = log(m) - log(n).
• log(m^n) = n × log(m).
• Logarithms help solve exponential equations.