Worksheets › Class 9 › Logarithms (Advanced)
Class 9 · Mathematics worksheetLogarithms (Advanced)
CBSE Mathematics. Optional Advanced level: exact values, product, quotient and power rules, change of base, log equations and extraneous roots, pH and Richter scale. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
The value of log₂ 16 is:
- −4
- 5
- 8
- 4
Answer
(d) 4
16 = 2⁴
- 2.
log₅ 1375 + log₅ 5 − log₅ 11 equals:
- 8
- 3
- 4
- 5
Answer
(c) 4
log₅ (1375 × 5 ÷ 11) = log₅ 625 = 4
- 3.
logₐ 1 equals (a > 0, a ≠ 1):
- a
- undefined
- 1
- 0
Answer
(d) 0
a⁰ = 1
Section B · short answer
- 4.
Write as a single logarithm: 3 + log₂ 14.
Answer
log₂ 112
3 = log₂ 8; log₂ 8 + log₂ 14 = log₂ (8 × 14)
- 5.
Find the exact value of log₂₅ 5.
Answer
1/2
25 = 5² and 5 = 5¹, so the value is 1/2
Section C · long answer
- 6.
(a) On the Richter scale, how many times as strong is an earthquake of magnitude 7 as one of magnitude 3? (b) A solution has [H⁺] = 10⁻⁴ mol per litre. Find its pH, given pH = −log₁₀ [H⁺]. (c) Another solution is 10 times as acidic. Find its pH.
Answer
(a) 10,000; (b) 4; (c) 3
(a) 10⁴; (b) −log₁₀ 10⁻⁴ = 4; (c) [H⁺] is 10¹ times larger, so the pH falls by 1
Fresh sheets for your child
In the app, every Logarithms (Advanced) sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.