Exponential and Logarithm Test

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, if b^y = x, then log_b(x) = y.

Front

Convert the exponential equation 2^3 = 8 into logarithmic form.

Back

log_2(8) = 3.

Front

What is the range of the function y = log_b(x)?

Back

The range is (-∞, ∞) for all logarithmic functions.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to produce a given number. In log_b(x), b is the base.

Front

What is the product rule for logarithms?

Back

log_b(MN) = log_b(M) + log_b(N).

Front

What is the quotient rule for logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N).

Front

What is the power rule for logarithms?

Back

log_b(M^p) = p * log_b(M).

Front

What is an asymptote in the context of logarithmic functions?

Back

An asymptote is a line that a graph approaches but never touches. For y = log_b(x), the vertical asymptote is at x = 0.

Front

What does it mean for a logarithmic function to be increasing?

Back

A logarithmic function is increasing if, as x increases, the value of log_b(x) also increases.