Exponents and Logarithms Flashcards

Vocabulary flashcards for exponents and logarithms chapter.

Exponential Function

A function where the unknown appears in the exponent, generally in the form f(x) = a^x.

Logarithm

The inverse operation to exponentiation, answering the question: 'What exponent do I have to raise a to in order to get b?'

Asymptote

A line that a function gets increasingly close to but never reaches.

Growth Factor

The fixed factor by which a value changes as time increases by a fixed value in an exponential function.

Euler's Number (e)

A mathematical constant approximately equal to 2.71828, serving as the base of the natural logarithm.

Common Logarithm

Logarithm with base 10, often written as log x.

Natural Logarithm

Logarithm with base e, often written as ln x.

Cancellation Principles (Logarithms)

loga(a^x) = x and a^(loga(x)) = x

Change of Base Rule (Logarithms)

logb(a) = logc(a) / log_c(b)

Exponential Growth

A model where a quantity increases over time. N = Ba^(t/k), a > 1

Exponential Decay

A Model where a quantity decreases over time. N = Ba^(t/k), 0< a < 1

Base

In the expression a^n, 'a' is the base.

Exponent

In the expression a^n, 'n' is the exponent or power.

Logarithm of a Product

loga(xy) = loga(x) + log_a(y) for x, y > 0

Logarithm of a Quotient

loga(x/y) = loga(x) - log_a(y) for x, y > 0

Logarithm of a Reciprocal

loga(1/x) = -loga(x) for x > 0

loga(x)^-1 = - loga(x)

Logarithm of a Power

loga(x^p) = p*loga(x) for x > 0

Logarithm of 1

log_a(1) = 0