Logarithms

Front

What is a logarithm?

Back

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

Front

What is the base of a logarithm?

Back

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

Front

What is the logarithmic form of the equation 5^2 = 25?

Back

log_5(25) = 2.

Front

What is the value of log_4(1)?

Back

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

Front

What transformation does y = log(x + 3) represent?

Back

A left shift of 3 units on the graph.

Front

What is the domain of the function y = log(x)?

Back

(0, ∞), since logarithms are only defined for positive numbers.

Front

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

Back

(-∞, ∞), as logarithmic functions can take any real value.

Front

How do you evaluate log_10(1000)?

Back

3, because 10^3 = 1000.

Front

What is the product rule of logarithms?

Back

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

Front

What is the quotient rule of logarithms?

Back

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