Mathematics: Indices and Logarithms

This set of flashcards covers key vocabulary and concepts related to Indices and Logarithms, including definitions, rules, and properties.

Indices

A number that shows how many times to multiply the base by itself.

Logarithm

The power to which a number must be raised to obtain another number.

Laws of Indices

Rules that describe how to manipulate powers and exponents.

Product Law (of Indices)

When multiplying two powers with the same base, you add the exponents.

Quotient Law (of Indices)

When dividing two powers with the same base, you subtract the exponents.

Power Law (of Indices)

When raising a power to another power, you multiply the exponents.

Base of a Logarithm

The number that is raised to a power in order to produce another number in logarithms.

Exponential Equation

An equation in which variables occur as exponents.

Change of Base Rule

A formula for expressing logarithm in terms of logarithms of a different base.

Identity Property (of Logarithms)

log_b(b) = 1, indicates that a logarithm of the base to itself equals one.

Zero Property (of Logarithms)

log_b(1) = 0, indicates that a logarithm of 1 is always zero.

Power Property (of Logarithms)

log_b(a^n) = n * log_b(a), allows you to bring the exponent in front.

Inverse Rule (of Logarithms)

If y = log_b(x), then b^y = x, shows the relationship between exponential and logarithmic functions.

Reciprocal Rule (of Logarithms)

log_b(x^(-1)) = -log_b(x), indicates the logarithm of the reciprocal.

Injective Function

A function that maps distinct inputs to distinct outputs; one-to-one function.

Surjective Function

A function that covers all possible outputs in its codomain; onto function.