CAT Logarithms & Exponents questions 55 since 2017

Across the 24 CAT papers from 2017 to 2025, Logarithms & Exponents was asked 55 times, in 23 of the 24 papers. CAT asks about 2.3 Logarithms & Exponents questions per paper on average; in 2022–2025 it was 2.3 per paper, against 2.1 in the four years before (steady). Below is how often it appeared each year, the ideas CAT keeps reusing, and every question with its answer.

How many Logarithms & Exponents questions come in CAT each year?

Logarithms & Exponents ideas CAT has repeated

• Writing a number as m^n: n must divide every prime exponent 3 questions, 2018–2024
• Equate exponents of each prime on both sides 3 questions, 2019–2025
• Exponential equation turned into a quadratic in a^x 6 questions, 2017–2025
• Set equal powers or logs to a common k and take logs 4 questions, 2017–2020
• Change of base: log_a b = 1 / log_b a 5 questions, 2018–2021
• Chained logs telescope via change of base 3 questions, 2020–2024
• Logs with bases that are powers of one base: convert to a common base 5 questions, 2017–2025
• Compare powers by summing exponents or taking logs 4 questions, 2018–2025

All Logarithms & Exponents questions, newest first

CAT 2025

• CAT 2025 Slot 3 · QA Q4 If ( x ^ 2 + 1 x ^ 2 ) = 25 and x > 0 , then the value of…
• CAT 2025 Slot 3 · QA Q7 The sum of all possible real values of x for which log _ x…
• CAT 2025 Slot 3 · QA Q9 If 12 ^ 12 x × 4 ^ 24 x + 12 × 5 ^ 2 y = 8 ^ 4 z × 20 ^ 12 x…
• CAT 2025 Slot 2 · QA Q2 If log _ 64 x ^ 2 + log _ 8 √( y ) + 3 log _ 512 ( √( y ) z…
• CAT 2025 Slot 2 · QA Q5 If 9 ^ x ^ 2 + 2 x - 3 - 4 ( 3 ^ x ^ 2 + 2 x - 2 ) + 27 = 0…
• CAT 2025 Slot 1 · QA Q3 The number of distinct integers n for which log _(1/4)(n^2-7…
• CAT 2025 Slot 1 · QA Q19 For any natural number k , let a_k=3^k . The smallest…

CAT 2024

• CAT 2024 Slot 3 · QA Q3 If (a+b √(3))^2=52+30 √(3) , where a and b are natural…
• CAT 2024 Slot 3 · QA Q16 If 3^a=4,4^b=5,5^c=6,6^d=7,7^e=8 and 8^f=9 , then the value…
• CAT 2024 Slot 3 · QA Q22 The sum of all distinct real values of x that satisfy the…
• CAT 2024 Slot 2 · QA Q3 If m and n are natural numbers such that n>1 , and m^n=2^25…
• CAT 2024 Slot 2 · QA Q9 If a, b and c are positive real numbers such that a>10 ≥ b ≥…
• CAT 2024 Slot 2 · QA Q13 If (x+6 √(2))^1/2-(x-6 √(2))^1/2=2 √(2) , then x equals
• CAT 2024 Slot 1 · QA Q2 If (a+b √(n)) is the positive square root of (29-12 √(5))…
• CAT 2024 Slot 1 · QA Q3 The sum of all real values of k for which (1/8)^k…
• CAT 2024 Slot 1 · QA Q22 If x is a positive real number such that 4 log _10 x+4 log…

CAT 2023

• CAT 2023 Slot 3 · QA Q1 For a real number x , if 1/2, (log _3(2^x-9))/(log _3 4)…
• CAT 2023 Slot 3 · QA Q2 Let n and m be two positive integers such that there are…
• CAT 2023 Slot 3 · QA Q4 If x is a positive real number such that x^8+(1/x)^8=47…
• CAT 2023 Slot 3 · QA Q7 Let n be any natural number such that 5^n-1 3^n+1 . Then…
• CAT 2023 Slot 2 · QA Q1 Let a, b, m and n be natural numbers such that a>1 and b>1…
• CAT 2023 Slot 2 · QA Q2 The sum of all possible values of x satisfying the equation…
• CAT 2023 Slot 2 · QA Q5 For some positive real number x , if log _√(3)(x)+(log…
• CAT 2023 Slot 1 · QA Q1 If x and y are positive real numbers such that log…
• CAT 2023 Slot 1 · QA Q3 If √(5 x+9)+√(5 x-9)=3(2+√(2)) , then √(10 x+9) is equal to

CAT 2022

• CAT 2022 Slot 3 · QA Q11 If (√(7/5))^3 x-y=875/2401 and ((4 a)/b)^6 x-y=((2 a)/b)^y-6…
• CAT 2022 Slot 2 · QA Q14 The number of distinct integer values of n satisfying (4-log…
• CAT 2022 Slot 2 · QA Q17 The number of integer solutions of the equation…

CAT 2021

• CAT 2021 Slot 3 · QA Q6 For a real number a, if log _15 a+log _32 a(log _15 a)(log…
• CAT 2021 Slot 3 · QA Q20 If n is a positive integer such that ([7]10)([7]10)^2…
• CAT 2021 Slot 2 · QA Q2 If log_2[3 + log_34 + log_4(x - 1)] - 2 = 0 then 4x equals answer only
• CAT 2021 Slot 1 · QA Q4 If 5 - log _10 √(1+x)) + 4 log _10 √(1-x)) = log _10 11-x^2)… answer only

CAT 2020

• CAT 2020 Slot 3 · QA Q3 Let log_a30 = A, log_a 5/3 = -B and log_2a = 1/3 , then… answer only
• CAT 2020 Slot 3 · QA Q10 2×4×8×16(log_24)^2(log_48)^3(log_816)^4 equals answer only
• CAT 2020 Slot 2 · QA Q5 The value of log_a a/b + log_b b/a , for 1 < a ≤ b cannot be… answer only
• CAT 2020 Slot 1 · QA Q5 If log_4 5 = (log_4 y) (log_6 √5), then y equals
• CAT 2020 Slot 1 · QA Q6 The number of real-valued solutions of the equation 2^x +…
• CAT 2020 Slot 1 · QA Q9 If x = (4096)^7+4√3, then which of the following equals 64?
• CAT 2020 Slot 1 · QA Q21 If y is a negative number such that 2 y^2log_35 = 5 log_23…

CAT 2019

• CAT 2019 Slot 2 · QA Q1 The real root of the equation 2^6x + 2^3x+2 - 21 = 0 is answer only
• CAT 2019 Slot 2 · QA Q19 If x is a real number ,then log_e(4x - x^2)/3 is a real… answer only
• CAT 2019 Slot 1 · QA Q24 If m and n are integers such that ( √(2) )^19 3^4 4^2 9^m… answer only
• CAT 2019 Slot 1 · QA Q26 Let x and y be positive real numbers such that log_5(x + y)… answer only

CAT 2018

• CAT 2018 Slot 2 · QA Q9 If p^3 = q^4 = r^5 = s^6, then the value of log_s (pqr) is… answer only
• CAT 2018 Slot 2 · QA Q34 1log_2100 - 1log_4100 + 1log_5100 - 1log_10100 + 1log_20100… answer only
• CAT 2018 Slot 1 · QA Q11 If x is a positive quantity such that 2^x = 3 log_52 , then… answer only
• CAT 2018 Slot 1 · QA Q12 If log_1281 = p, then 3( (4 - p)/(4 + p) ) is equal to answer only
• CAT 2018 Slot 1 · QA Q25 Given that x^2018 y^2017 = 1/2 and x^2016 y^2019 = 8, the… answer only
• CAT 2018 Slot 1 · QA Q27 If log_2(5 + log_3a) = 3 and log_5(4a + 12 + log_2b) = 3… answer only

CAT 2017

• CAT 2017 Slot 2 · QA Q22 If x is a real number such that log_35 = log_5(2 + x), then… answer only
• CAT 2017 Slot 2 · QA Q25 If 9^x - ( 1/2 ) – 2^2x – 2 = 4^x – 3^2x – 3, then x is answer only
• CAT 2017 Slot 2 · QA Q26 If log(2^a × 3^b × 5^c) is the arithmetic mean of log(2^2 ×… answer only
• CAT 2017 Slot 1 · QA Q21 Suppose, log_3x = log_12y = a, where x, y are positive… answer only
• CAT 2017 Slot 1 · QA Q23 The value of log_0.008√5 + log_√381 – 7 is equal to answer only
• CAT 2017 Slot 1 · QA Q24 If 9^2x – 1 – 81^x-1 = 1944, then x is answer only

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