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NDA Logarithms questions with solutions

Logarithms and indices. 11 questions from our 2016–2025 NDA pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Logarithms for CAT

NDA 2025

/are correct (all logarithms defined, bases positive and not equal to 1)? 1. log ab·log bc=log ac 2. log (x+y)=log x+log y for all positive x,yNDA 2025 Maths · medium

NDA 2023

If log 2x+log 4x+log 16x=7, then x equalsNDA 2023 Maths · medium
The solution set of log 1/2(x-1)>1 isNDA 2023 Maths · hard
Log 10x<0 if and only if 0<x<1. 2. log ab=-log ba for all positive a,b different from 1.NDA 2023 Maths · medium

NDA 2019

If log ab=2 and log bc=3, then log ac equalsNDA 2019 Maths · easy
The sum of all the solutions of log 2(x^2-x)=1 isNDA 2019 Maths · medium
Log 10x<0 for every x with 0<x<1. 2. If log ax>log ay then x>y, for every valid base a.NDA 2019 Maths · medium

NDA 2018

Given log 102=0.3010, how many digits does 2^20 have?NDA 2018 Maths · medium
Log (ab)=log a+log b for all non-zero real numbers a and b. 2. log a b·log b a=1 for a,b>0 and a,b≠1.NDA 2018 Maths · medium

NDA 2016

If log x 27=3/2, then x is equal toNDA 2016 Maths · medium
If log 102=a and log 103=b, then log 1072 is equal toNDA 2016 Maths · easy