Logs | A-Level Maths

Exponential graph

Rules of Logarithms

1. log(a) + log(b) = log(ab)
2. log(a) - log(b) = log(a/b)
3. log(a)ⁿ = nlog(a)
4. log_a(a) = 1
5. If log_a(x) = 5 then x = a⁵

Power rule

Question 1

hint: use rule 3

Adding and subtracting logs

Question 2a

Question 2b

Solving exponential equations

Question 3a

Question 3b

Solving log equations

Question 4a

Question 4b

Answers x=0.5, y=0.6

Question 4c

Answers: x=1, y=5/3

Question 4d

Question 4e

Modelling with logs

Question 5a

Question 5b

Problem solving

Question 6a