Evaluating & Analyzing Log functions &Graphs

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, expressed as y = log_b(x), where b is the base and x is the argument.

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(x), b is the base.

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverse of exponential functions. If y = b^x, then x = log_b(y).

Front

What is the logarithmic identity log_b(b) = ?

Back

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

Front

What is the value of log_b(1)?

Back

log_b(1) = 0, because any number raised to the power of 0 is 1.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

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 logarithmic functions, the vertical asymptote is typically at x = 0.

Front

Evaluate log_6(6^3).

Back

log_6(6^3) = 3, because the logarithm of a number raised to a power is the exponent.

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is (0, ∞), meaning it only accepts positive real numbers.

Front

What is the range of a logarithmic function?

Back

The range of a logarithmic function is (-∞, ∞), meaning it can take any real number as its output.