NDA 2019 Maths · Mathematics · Logarithms · 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.

Single correct option

Consider the following statements:
1.

\log_{10}x<0

for every

x

with

0<x<1

.
2. If

\log_ax>\log_ay

then

x>y

, for every valid base

a

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (A) 1 only

Statement 1: for

0<x<1

we have

x<10^0

, so

\log_{10}x<0

; it is true. Statement 2 is false because the logarithm is a decreasing function when the base satisfies

0<a<1

. For example

\log_{1/2}\dfrac14=2>\log_{1/2}\dfrac12=1

but

\dfrac14<\dfrac12

. Hence only statement 1 is correct.

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake