3.3 Solve logarithmic equations

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, if b^y = x, then log_b(x) = 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, where k is the new base.

Front

What is the product rule for logarithms?

Back

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

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for 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 for x?

Back

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

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

How can you combine logarithmic expressions using the product rule?

Back

You can combine logarithmic expressions by adding them: log_b(m) + log_b(n) = log_b(m * n).

Front

How can you simplify the expression log_b(m) - log_b(n)?

Back

You can simplify it using the quotient rule: log_b(m) - log_b(n) = log_b(m / n).

Front

What is the value of log_10(1000)?

Back

The value of log_10(1000) is 3, because 10^3 = 1000.