Example 1 · level 1
Find log to base 3 of 243.
Show solution
- 3 = 3^1, 243 = 3^5.
- (3^1)^y = 3^5 → 1y = 5.
- y = 5.
Answer: 5
CA FOUNDATION: QUANTITATIVE APTITUDE · RATIO AND PROPORTION, INDICES, LOGARITHMS
Logarithms: evaluate log values
log_b(x) = y means b^y = x. log a + log b = log(ab). log_(c^p)(c^q) = q/p.
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Worked examples
Example 2 · level 2
Find the value of log 4 + log 250 (logarithms to base 10).
Show solution
- log 4 + log 250 = log(4 × 250) = log 1,000.
- 1,000 = 10^3, so the value is 3.
Answer: 3
Example 3 · level 3
Find log to base 8 of 128. Give a fraction if needed.
Show solution
- 8 = 2^3, 128 = 2^7.
- (2^3)^y = 2^7 → 3y = 7.
- y = 7/3.
Answer: 7/3