Solving Logarithmic Equations

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 inverse of a logarithmic function?

Back

The inverse of a logarithmic function is an exponential function.

Front

How do you solve the equation log_b(x) = y?

Back

To solve log_b(x) = y, rewrite it in exponential form: x = b^y.

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 the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.

Front

What is the common logarithm?

Back

The common logarithm is the logarithm to the base 10, denoted as log(x).

Front

How do you simplify log_b(mn)?

Back

log_b(mn) = log_b(m) + log_b(n) (Product Rule).

Front

How do you simplify log_b(m/n)?

Back

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

Front

How do you simplify log_b(m^n)?

Back

log_b(m^n) = n * log_b(m) (Power Rule).