3.3 Solve logarithmic equations

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.

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.

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

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

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

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

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

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

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

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