Practice: Intro to Log 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 obtain a given number. For example, in log_b(a), b is the base.

Front

What is the domain of log(x)?

Back

The domain of log(x) is (0, ∞), meaning logarithms are only defined for positive real numbers.

Front

What is the general shape of a logarithmic function?

Back

Logarithmic functions increase slowly and have a vertical asymptote at x = 0.

Front

What is the product rule of logarithms?

Back

log_b(mn) = log_b(m) + log_b(n), where m and n are positive real numbers.

Front

What is the quotient rule of logarithms?

Back

log_b(m/n) = log_b(m) - log_b(n), where m and n are positive real numbers.

Front

What is the power rule of logarithms?

Back

log_b(m^p) = p * log_b(m), where m is a positive real number and p is any real number.

Front

What is the asymptote of y = log_b(x)?

Back

The vertical asymptote of y = log_b(x) is at x = 0.

Front

How do you convert a logarithmic equation to an exponential form?

Back

If log_b(a) = c, then it can be rewritten as b^c = a.

Front

What is log(1)?

Back

log(1) = 0 for any base, because any number raised to the power of 0 equals 1.

Front

What is the value of log_b(b)?

Back

log_b(b) = 1, because any number raised to the power of 1 equals itself.