Logarithms, Diploma Style

Log laws, change of base, exponential equations, pH and earthquake scales, and compound interest solved for time.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

• math30 1 logarithms

The questions

1. What is the value of log₂ 48 − log₂ 3?
2. Evaluate log₃ 20, correct to the nearest hundredth.
3. Which single logarithm equals 3 log x + log 4 − log 2?
4. Solve 2ˣ⁺¹ = 3ˣ, correct to the nearest hundredth.
5. What is the solution of 9ˣ = 27ˣ⁻¹?
6. The pH of a solution is pH = −log[H⁺]. A sample has [H⁺] = 3.2 × 10⁻⁴ mol/L. What is its pH, correct to the nearest hundredth?
7. On a magnitude scale where each unit is a factor of 10 in amplitude, how many times as great is the amplitude of a magnitude 7.2 earthquake as that of a magnitude 5.8 one?
8. $2 000 is invested at 4.5% a year, compounded monthly. How many years will it take to grow to $3 000? Give the answer correct to the nearest tenth of a year.
9. What is the domain of y = log₃(x − 2) + 1?
10. If log_b 2 = m and log_b 3 = n, which expression equals log_b 12?

Answer these free