Q1
What is a logarithm?
AThe inverse of exponentiation
BThe same as multiplication
CThe same as addition
DNothing related to exponents
ICSEClass 9 (ICSE)MathematicsCh 8 · Topic 1
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.
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• 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.