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XAT 2021 Logarithms — Previous Year Question

Paper

XAT 2021

Section

Quantitative

Topic

Logarithms

Difficulty

Medium

Question

XAT 2021

If log⁡4m+log⁡4n=log⁡2(m+n)\log_{4} m + \log_{4} n = \log_{2}(m+n) where m and n are positive real numbers, then which of the following must be true?

1m+1n=1\frac{1}{m} + \frac{1}{n} = 1

m = n

m2+n2=1m^2 + n^2 = 1

1m+1n=2\frac{1}{m} + \frac{1}{n} = 2

No values of m and n can satisfy the given equation

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