Purpose: Self-check your understanding. This quiz is not graded .
Click "Check Answer" for instant feedback and "Show Solution" for detailed explanations with rendered formulas.
6.2 — Introduction to Logarithms
Question 1
Evaluate: \( \log_2(64) \)
Check Answer
Show Solution
Solution:
\( 2^? = 64 \). Since \( 2^6 = 64 \), \( \log_2(64) = 6 \).
Question 2
Evaluate: \( \log_5\left(\frac{1}{25}\right) \)
Check Answer
Show Solution
Solution:
\( 5^? = \frac{1}{25} = 5^{-2} \). So \( \log_5\left(\frac{1}{25}\right) = -2 \).
Question 3
\( \log_3(81) = \)
Check Answer
Show Solution
Solution:
\( 3^4 = 81 \), so \( \log_3(81) = 4 \).
6.4–6.5 — Log Laws
Question 4
\( \log_2(8) + \log_2(4) = \)
Check Answer
Show Solution
Solution:
By the product law: \( \log_2(8) + \log_2(4) = \log_2(8 \times 4) = \log_2(32) = 5 \).
Or directly: \( 3 + 2 = 5 \).
Question 5
Which expression equals \( \log\left(\frac{x^3}{y^2}\right) \)?
Check Answer
Show Solution
Solution:
By log laws: \( \log\left(\frac{x^3}{y^2}\right) = \log(x^3) - \log(y^2) = 3\log(x) - 2\log(y) \).
MHF4U — Advanced Functions, Grade 12 | Ontario Curriculum 2007 (Revised)