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If the following numbers are put in order from smallest to largest then which of the numbers will be the middle number on the list?

A. $4\log(3)$

B. $0.5\log(144)$

C. $\log(4)+\log(5)$

D. $\log(4)−\log(5)$

E. $\log(5−4)$

D is the lowest (<0) and E is the second lowest (0) how can I order the next few. I guess that A. is the highest.

user3371583
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1 Answers1

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$$4\log(3) = \log(3^4)=\log(81)$$ $$0.5\log(144)=0.5 \log(12^2)=\log(12)$$ $$\log(4)+\log(5) =\log(4 \cdot 5) = \log(20) $$ $$\log(4)-\log(5) =\log(4 / 5) $$ $$\log(5-4) =\log(1) $$

Log is a strictly increasing function (i.e. $\forall x, y \in \mathbb{R}_+^*,\quad x < y \implies \log(x) < \log(y). $

user3371583
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