Logarithms I — O/L Mathematics

What must I remember about Logarithms I?

• Logarithm definition: The logarithm of a positive number y to a positive base a (a ≠ 1) is the exponent x to which a must be raised to equal y: a^x = y ⟺ log_a y = x.
• Product law of logarithms: log_a (xy) = log_a x + log_a y.
• Quotient law of logarithms: log_a (x / y) = log_a x - log_a y.
• Power law of logarithms: log_a (x^k) = k log_a x.
• Base identities: log_a a = 1; log_a 1 = 0; a^{log_a x} = x.

Test yourself (1 minute)

1. The pseudo-distributive logarithm error

   log(x + y) NEVER equals log x + log y; similarly log(x - y) NEVER equals log x - log y.

2. Quotient law vs fraction of logs

   log(x / y) = log x - log y, which is completely different from (log x) / (log y).

3. Converting between forms

   Master switching rapidly between index form (2⁵ = 32) and log form (log₂ 32 = 5) for Paper 1 Part A questions.

Practise Logarithms I questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 18)

What should I study first?

What comes next?

Next in the syllabus

Where does Logarithms I fit in the syllabus?

Grade 10 · Term 2