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JEE Advanced

Exam: JEE Advanced
Subject: Mathematics
Chapter: Basics of Mathematics

JEE Advanced · Mathematics · Basics of Mathematics

Which of the following is correct?

Which of the following is correct?

Options

A $\log _5(\sqrt{7 \sqrt{7 \sqrt{7 \ldots \ldots}}})>1$
B $\log _{(\sqrt{7}-\sqrt{6})}(\sqrt{3}-\sqrt{2}) < 1$
C $\log _3 10>\log _{10} 70$
D $\log _3(3+\sqrt{2})>\log _2(2-\sqrt{2})$

Correct answer

D. $\log _3(3+\sqrt{2})>\log _2(2-\sqrt{2})$

Step-by-step solution

(1)

\log _5(\sqrt{7 \sqrt{7 \sqrt{7 \ldots \ldots .}}})=\log _5 7>1

(2)

\frac{1}{\sqrt{3}+\sqrt{2}} < \frac{1}{\sqrt{7}+\sqrt{6}} \Rightarrow \sqrt{3}-\sqrt{2}>\sqrt{7}-\sqrt{6}

(3)

\log _3 10>2

and

\log _{10} 70 < 2

(4)

\log _3(3+\sqrt{2})>1

and

\log _2(2-\sqrt{2}) < 1

.

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