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.

Tags

CCSS.HSF.BF.B.5

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 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

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.

Tags

CCSS.HSF.BF.B.5

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^n) = n * log_b(m).

Front

Solve: log_2(8) = ?

Back

3, because 2^3 = 8.

Tags

CCSS.HSF.BF.B.5

Front

Solve: log_10(100) = ?

Back

2, because 10^2 = 100.

Tags

CCSS.HSF.BF.B.5

Front

Solve: log_5(25) = ?

Back

2, because 5^2 = 25.

Tags

CCSS.HSF.BF.B.5