Solving Equations with Logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number must be raised to obtain another number. For example, if b^y = x, then log_b(x) = y.

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(x), b is the base.

Front

What is the logarithmic identity for multiplication?

Back

log_b(M * N) = log_b(M) + log_b(N) for any positive numbers M and N.

Front

What is the logarithmic identity for division?

Back

log_b(M / N) = log_b(M) - log_b(N) for any positive numbers M and N.

Front

What is the logarithmic identity for exponentiation?

Back

log_b(M^k) = k * log_b(M) for any positive number M and any real number k.

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 value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.

Front

What is the value of log_5(25)?

Back

log_5(25) = 2, because 5^2 = 25.