How many Logarithms questions come in CAT Quant?

About 0.9 questions in a 22-question Quant section, worth roughly 3 marks. Logarithms appeared in 22 of the 24 CAT papers from 2017 to 2025, 31 questions in all, which ranks it 14 of 25 Quant chapters.

Are Logarithms questions in CAT MCQ or TITA?

36% of the Logarithms questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.

What types of Logarithms questions does CAT ask?

CAT keeps returning to 6 question shapes in Logarithms: Solve a log equation; Equal powers, several bases; Inequalities, domains and counting; Logs tangled with exponents; Change of base, then rearrange; Just evaluate it.

Logarithms for CAT: Formulas, Weightage & Question Types

A log is an exponent: log equations, change of base, and inequalities with domains.

Logarithms formula sheet

Everything CAT needs from Logarithms, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place. Throughout, bases are positive and not 1, and arguments are positive.

What it means


Definition	$\log_b a = x \iff b^x = a$
So	$b^{\log_b a} = a$
Always	$\log_b 1 = 0$ and $\log_b b = 1$

The laws — they are the exponent laws, re-read


Product	$\log(mn) = \log m + \log n$
Quotient	$\log\dfrac{m}{n} = \log m - \log n$
Power	$\log(m^p) = p\log m$
A sum of logs	is the log of a product — always combine before solving

Changing the base — the engine of the chapter


General	$\log_b a = \dfrac{\log_c a}{\log_c b}$
Flip	$\log_b a = \dfrac{1}{\log_a b}$
Powers in both places	$\log_{b^p}(a^q) = \dfrac{q}{p}\log_b a$
Swap the exponents	$a^{\log_b c} = c^{\log_b a}$
A chain telescopes	$\log_a b \cdot \log_b c \cdot \log_c d = \log_a d$

When several powers are equal


If $a^x = b^y = c^z = k$	$\dfrac{1}{x} = \log_k a$ , $\dfrac{1}{y} = \log_k b$ , $\dfrac{1}{z} = \log_k c$
Which makes	sums and differences of $\dfrac{1}{x}$ into logs of products and quotients

Sign and direction — where the traps live


$\log_b a > 0$	when $a$ and $b$ are on the same side of 1
$\log_b a < 0$	when they are on opposite sides
Base $> 1$	the log increases, so inequalities keep their direction
Base between 0 and 1	the log decreases, so inequalities flip
Domain	the argument must be strictly positive, and the base positive and $\neq 1$

Useful values


$\log_{10} 2 \approx 0.301$	$\log_{10} 3 \approx 0.477$
$\log_2 3 \approx 1.585$	$\log_2 10 \approx 3.322$

The 6 Logarithms question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

01
Solve a log equation
02
Equal powers, several bases
03
Inequalities, domains and counting
04
Logs tangled with exponents
05
Change of base, then rearrange
06
Just evaluate it

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Logarithms in CAT: quick answers

How many Logarithms questions come in CAT Quant?: About 0.9 questions in a 22-question Quant section, worth roughly 3 marks. Logarithms appeared in 22 of the 24 CAT papers from 2017 to 2025, 31 questions in all, which ranks it 14 of 25 Quant chapters.
Are Logarithms questions in CAT MCQ or TITA?: 36% of the Logarithms questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Logarithms questions does CAT ask?: CAT keeps returning to 6 question shapes in Logarithms: Solve a log equation; Equal powers, several bases; Inequalities, domains and counting; Logs tangled with exponents; Change of base, then rearrange; Just evaluate it.

Logarithms for CAT: Formulas, Weightage & Question Types

Logarithms formula sheet

The 6 Logarithms question types CAT repeats

Is Logarithms costing you marks?

Logarithms in CAT: quick answers

More Algebra for CAT