Logarithms

Evaluate logarithms and understand their relationship to exponents.

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

What this covers

• logarithms
• math30 1 logarithms

The questions

1. log₂(8) = ?
2. log₁₀(1000) = ?
3. log₅(1) = ?
4. Which is equivalent to log_b(x) = y?
5. log₃(9) = ?
6. log₄(64) = ?
7. Which rule correctly expands log(A × B)?
8. Simplify: log₃(3⁵)
9. log₁₀(100) = ?
10. An investment of $5 000 grows at 6% per year, compounded annually. After how many years is it first worth $8 000? Give your answer in years, rounded to one decimal place.
11. Solve for x: log₂(x) = 5.
12. Which expression is equivalent to log(a) + log(b)?
13. An investment of $3000 grows at 5% per year, compounded annually. After how many years is it first worth $4500? Give your answer in years, rounded to one decimal place.

Answer these free