명제의 증명과 절대부등식 연습문제 — Sundstrom, Mathematical Reasoning · 3.3절 · 11a번

Sundstrom, Mathematical Reasoning · 3.3절 · 11a번영어 원문

Justify your conclusion for each of the following.

Is the base 2 logarithm of 32, $\log_2 (32)$ , a rational number or an irrational number?

정답·풀이 보기 (영어 원문)

Recall that $\log _2 (32)$ is the real number $a$ such that $2^a = 32$ . That is, $a = \log _2 (32)$ means that $2^a = 32$ . If we assume that $a$ is rational, then there exist integers $m$ and $n$ , with $n \ne 0$ , such that $a = \dfrac{m}{n}$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 3.3절 · 6a번영어 원문

Are the following statements true or false? Justify each conclusion.

For each positive real number $x$ , if $x$ is irrational, then $x^2$ is irrational.

다 풀었으면 정답 확인

This statement is false. A counterexample is $x = \sqrt{2}$ .

이 문제로 이어서 풀기

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