AP PreCalc 2.9-2.12 Logarithmic Functions and their properties

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

Front

What is the value of log_4(1)?

Back

0, because any number raised to the power of 0 equals 1.

Front

Solve for x: log(x + 6) = 1.

Back

x = 4, because 10^1 = x + 6.

Front

Evaluate log_8(8).

Back

1, because 8^1 = 8.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value. For example, in log_b(a), b is the base.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

What is the product property of logarithms?

Back

log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient property of logarithms?

Back

log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power property of logarithms?

Back

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

Front

What does DNE stand for in logarithmic terms?

Back

DNE stands for 'Does Not Exist', indicating that the logarithm of a non-positive number is undefined.