Four Comparisons

★ 6/10functions Monotonicity Logarithms AM-GM inequality

Problem

Determine, with proof, which of the following are true:

1. $1.9^2 < 2^{1.9}$ ; 2. $2^{2.9} < 2.9^2$ ; 3. $\log_7 4 < \log_{12} 7$ ; 4. $\log_7 4 + \log_{12} 7 < \sqrt{2}$ .

Answer

Solution

Difficulty	6/10
Topics	functions, Monotonicity, Logarithms, AM-GM, inequality

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.