Solving Exponential and Logarithmic Equations

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent, e.g., 2^x = 8.

Front

What is a logarithmic equation?

Back

An equation that involves a logarithm of a variable, e.g., log_b(x) = y.

Front

What is the base of a logarithm?

Back

The number that is raised to a power to obtain a given value, e.g., in log_b(x), b is the base.

Front

What is the relationship between exponential and logarithmic functions?

Back

They are inverses of each other; if y = b^x, then x = log_b(y).

Front

How do you solve log_b(x) = y?

Back

Rewrite it in exponential form: x = b^y.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

What is the product property of logarithms?

Back

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

Front

What is the quotient property of logarithms?

Back

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

Front

What is the power property of logarithms?

Back

log_b(M^p) = p * log_b(M).

Front

How do you solve log_3(x - 5) = 2?

Back

Rewrite as x - 5 = 3^2, so x = 14.