반대수 그래프

가로축만 로그축인 반대수 그래프
세로축만 로그축인 반대수 그래프

과학공학에서 반대수 그래프(semi-log graph or semi-log plot)는 지수 함수 관계에 있는 데이터들을 나타내는 데 사용된다. 가로축 또는 세로축이 로그 스케일로 표현된다.

이 방법은 한 변수가 큰 폭으로 변하는 반면 다른 값은 작은 폭으로 변할 때 유용하다.[1]

지진학자 찰스 릭터는 "로그 그래프는 마법의 도구다"라고 말했다.[2]

꼴의 모든 그래프는 반대수지에 그릴 경우 직선을 나타낸다. 양변에 로그를 취하면 다음과 같기 때문이다.

log-lin은 세로축에 로그가 사용된 반대수 그래프를 말하며, lin-log는 가로축에 로그가 사용된 반대수 그래프를 말한다.

반대수지에서 격자 간격은 로그에 쓰이는 숫자가 아니라 로그값 자체에 비례한다. 즉 로그값을 계산한 다음에 lin-lin 격자에 그래프를 그린다고 생각하면 된다.

방정식

세로축이 로그축인 직선에 대한 방정식은

응용

물의 상태변화 그래프

물리학과 화학에서, 물을 포함한 다양한 물질의 상변화를 세로축이 압력에 대한 로그축, 가로축은 온도인 그래프로 나타낸다.

물의 Log-lin 압력–온도 상변화 그래프

2009년 돼지 인플루엔자 그래프

2009년 인플루엔자 범유행 당시 발병 수와 사망자 수 반대수 그래프. 세로축은 밑이 2인 로그축이다.

미생물 증가

생물학과 생명공학에서, 미생물 수의 무성생식에 의한 변화와 영양분 고갈은 보통 반대수지로 나타낸다. 시간을 독립변수, 세균 또는 미생물의 수 또는 질량을 종속변수인 로그축으로 나타내면 다음과 같다.

같이 보기

각주

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