If log 3 = A and log 7 = B, find log7 (9) in terms of A and B.

Key Concepts

Logarithmic Properties

Logarithmic properties are rules that govern the manipulation of logarithms. Key properties include the product rule (log_b(mn) = log_b(m) + log_b(n)), the quotient rule (log_b(m/n) = log_b(m) - log_b(n)), and the power rule (log_b(m^k) = k * log_b(m)). Understanding these properties is essential for simplifying logarithmic expressions and solving equations involving logarithms.

Change of Base Formula

The change of base formula allows us to express logarithms in terms of logarithms of a different base. It states that log_b(a) = log_k(a) / log_k(b) for any positive k. This formula is particularly useful when the logarithm's base is not easily computable, enabling us to convert it into a more manageable form using known logarithmic values.

Expressing Logarithms in Terms of Known Values

Expressing logarithms in terms of known values involves using given logarithmic values to rewrite other logarithmic expressions. In this case, we can use the values of log 3 = A and log 7 = B to find log 9 in terms of A and B. This technique often involves applying logarithmic properties and the change of base formula to derive the desired expression.