Mathematics 30 flashcards ~15 min

Exponents, Logarithms and Indices

About this deck

Exponents and logarithms are fundamental tools that appear throughout algebra, calculus, and science. This deck covers the core rules for multiplying, dividing, and raising powers, along with negative and fractional exponents. You'll also review logarithm properties, the natural logarithm, the change of base formula, and how exponential and logarithmic functions relate as inverses. A solid refresher for students working through algebra, precalculus, or any course involving exponential growth and decay.

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A number indicating how many times a base is multiplied by itself

The number being multiplied repeatedly

a^m × a^n = a^(m+n)

a^m ÷ a^n = a^(m−n)

(a^m)^n = a^(mn)

The reciprocal of the base raised to the positive exponent

A root, e.g. a^(1/n) = the nth root of a

The power to which a base must be raised to produce a given number

log_a(b) = x

A logarithm with base 10

A logarithm with base e (approximately 2.718)

log(xy) = log(x) + log(y)

log(x/y) = log(x) − log(y)

log(x^n) = n·log(x)

log_a(b) = log_c(b) / log_c(a)

A function of the form f(x) = a·b^x

Growth where a quantity increases at a rate proportional to its current value

Decrease where a quantity decreases at a rate proportional to its current value

2.71828

Another term for exponent, indicating repeated multiplication

A logarithmic function

Rewrite both sides with the same base and equate exponents (x = 3)

Expressing numbers as a value between 1 and 10 multiplied by a power of 10

Undefined

No, logarithms of negative numbers are undefined in the real number system

They are reflections of each other across the line y = x

An irrational root, such as √2, that cannot be simplified to a whole number