Solving Logarithmic Equations

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to produce a given number.

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 product rule of logarithms?

Back

The product rule states that log_b(m * n) = log_b(m) + log_b(n).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^p) = p * log_b(m).

Front

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

Back

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

Front

What is the definition of an exponential equation?

Back

An exponential equation is an equation in which a variable appears in an exponent.

Front

How do you solve an exponential equation of the form a^(x) = b?

Back

To solve a^(x) = b, take the logarithm of both sides: x = log_a(b).

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverses of exponential functions, meaning if y = b^x, then x = log_b(y).

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.