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XAT 2021 — QA & DI Question 1

LogarithmsEasy

If log4 m + log4 n = log2 (m + n) where m and n are positive real numbers, then which of the following must be true?

Answer & solution

  • A

    1m + 1n = 1

  • B

    m = n

  • C

    m2 + n2 = 1

  • D

    1m + 1n = 2

  • No values of m and n can satisfy the given equation

Solution

log4 mn = log2 (m + n)

mn = (m + n)

Squaring on both sides

m2 + n2 + mn = 0

Since m, n are positive real numbers, no value of m and n satisfy the above equations.

XAT 2021 QA & DI Q1: If log 4 m + log 4 n = log 2 (m + n) where m and n are positive real numbers, then which of the following must — Solution | TheCATExam