数学の基礎
移民・留学生・働く人のための豪州の日常語、スラング、生活手続き用語を、やさしい英語と8言語で解説します。
確認済み項目
35 件argument
noun真数
In maths, the input of a function, such as the number inside a logarithm.
In log₃(x + 2), the argument is x + 2 and it must be positive.
log₃(x + 2)では真数はx + 2で、正でなければならない。asymptote
noun漸近線
A line that a graph approaches more and more closely but does not reach.
The graph of y = 2ˣ has a horizontal asymptote at y = 0.
y = 2ˣのグラフはy = 0に水平漸近線をもつ。base
noun底（てい）
In maths, the number that is multiplied by itself in a power, or the number a logarithm is based on.
In 2⁵, the base is 2 and the exponent is 5.
2⁵では、底は2で指数は5だ。底の変換公式
The formula log_b(x) = log x ÷ log b, used to calculate logarithms in any base.
With the change of base formula, log₅ 20 = log 20 ÷ log 5.
底の変換公式により、log₅ 20 = log 20 ÷ log 5となる。common logarithm
noun常用対数
A logarithm with base 10, written log x.
The common logarithm of 1,000 is 3.
1,000の常用対数は3だ。複利
Interest calculated on the original amount and on the interest already added.
With compound interest, $1,000 at 5% grows to about $1,276 after five years.
複利では、1,000ドルを5%で5年預けると約1,276ドルになる。doubling time
noun倍増時間
The time it takes for a growing quantity to double.
If a population has a doubling time of 10 years, it is four times larger after 20 years.
倍増時間が10年の人口は、20年後に4倍になる。Euler's number
nounネイピア数 e
The mathematical constant e, about 2.718, used in continuous growth and natural logarithms.
Continuous growth models use Euler’s number, e.
連続的な成長のモデルにはネイピア数eが使われる。
exponent
noun指数
A small number written above another number to show how many times it is multiplied by itself.
In 5³, the exponent is 3.
5³では指数は3だ。指数関数的減少
Decrease by the same percentage over equal time periods.
The value of the car shows exponential decay of 15% a year.
その車の価値は年15%の指数関数的減少を示す。指数方程式
An equation in which the variable is in an exponent.
To solve the exponential equation 3ˣ = 81, write 81 as 3⁴.
指数方程式3ˣ = 81を解くには、81を3⁴と表す。指数関数
A function of the form f(x) = a·bˣ, where the variable is in the exponent.
Population growth can be modelled by an exponential function.
人口増加は指数関数でモデル化できる。指数関数的増加
Increase by the same percentage over equal time periods.
The bacteria show exponential growth, doubling every hour.
細菌は1時間ごとに倍になる指数関数的増加を示す。growth factor
noun成長因子（倍率）
The number b in an exponential model that each value is multiplied by, such as 1.05 for 5% growth.
A growth factor of 1.05 means a 5% increase each year.
成長因子1.05は毎年5%の増加を意味する。half-life
noun半減期
The time it takes for a quantity to fall to half its amount.
A substance with a half-life of 8 days has a quarter left after 16 days.
半減期が8日の物質は、16日後に4分の1が残る。index
noun根指数
In maths, the small number on a root sign showing which root to take, as in ³√8.
In ³√27, the index is 3, so we take the cube root.
³√27では根指数が3なので、立方根を求める。inverse function
noun逆関数
A function that reverses another function, written f⁻¹(x).
The inverse function of f(x) = 2x + 1 is f⁻¹(x) = (x − 1) ÷ 2.
f(x) = 2x + 1の逆関数はf⁻¹(x) = (x − 1) ÷ 2だ。logarithm
noun対数
The power to which a base must be raised to give a number: log_b(x) = y means bʸ = x.
log₂(8) = 3, because 2³ = 8.
2³ = 8なので、log₂(8) = 3だ。対数方程式
An equation that contains a logarithm of the variable.
To solve the logarithmic equation log₂ x = 5, rewrite it as x = 2⁵.
対数方程式log₂ x = 5を解くには、x = 2⁵と書き直す。対数関数
A function of the form f(x) = log_b(x), the inverse of an exponential function.
The graph of a logarithmic function rises slowly and never touches the y-axis.
対数関数のグラフはゆっくり増加し、y軸に触れることはない。対数目盛
A scale where each step represents multiplying by the same factor, such as 10.
The Richter scale for earthquakes is a logarithmic scale.
地震のリヒター・スケールは対数目盛だ。自然対数
A logarithm with base e, written ln x.
The natural logarithm of e² is 2.
e²の自然対数は2だ。負の指数
An exponent less than zero, meaning the reciprocal: a⁻ⁿ = 1/aⁿ.
A negative exponent gives a fraction: 2⁻³ = 1/8.
負の指数は分数になる：2⁻³ = 1/8。nth root
nounn乗根
A number that, raised to the power n, gives the original number.
The 4th root of 81 is 3, because 3⁴ = 81.
3⁴ = 81なので、81の4乗根は3だ。桁（オーダー）
The size of a number in powers of ten.
The two distances differ by three orders of magnitude, a factor of about 1,000.
2つの距離は3桁、つまり約1,000倍異なる。