Day 35 of 60 · Tue 3 Nov · Daily workbook · CAT in 26 days

Day 35: Logarithms & Indices + Routes & Optimisation Set + Literature & Arts RC

Day 35 of the free ThinkCAT 60-day CAT challenge: 5 logarithms & indices questions and 3 spaced-review QA questions, a full routes & optimisation DILR set (5 questions), a literature & arts RC passage (4 questions), plus para summary and para jumbles. Every question is a real CAT PYQ.

QA · 8
DILR · 5
VARC · 6
40 minutes
Real CAT questions

Concept card

Logarithms & Indices

Core formulas

log mn = log m + log n; log mᵏ = k log m
Change of base: logₐ x = log x / log a; logₐ x = 1/logₓ a
Chain: logₐ x × logₓ y = logₐ y
Same base: aˣ = aʸ ⇒ x = y (a > 0, a ≠ 1)

60-second shortcut · Chains collapse

log₂ 3 × log₃ 4 × log₄ 5 × log₅ 6 × log₆ 7 × log₇ 8 = log₂ 8 = 3.

Trap box

Looks like: log(a + b) = log a + log bActually: log a + log b = log(ab)
Looks like: aᵇ = 1 ⇒ b = 0Actually: Also a = 1, or a = −1 with b even

From the free Algebra Formula Sheet (PDF).

What's in Day 35

QA: Logarithms & Indices (5) + 3 spaced-review questions
DILR: Routes & Optimisation set, 5 questions
RC: Literature & Arts passage
VA: Para Summary, Para Jumbles

Year, slot and question number for each question appear with the answer key after you submit.

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