Just like indices, logarithms have laws that help simplify expressions and solve equations. These laws are closely related to the laws of indices.
▸ Product Law of Logarithms — The logarithm of a product is the sum of the logarithms.
Example: log_a(MN) = log_a(M) + log_a(N). For example, log 3 + log 4 = log(3*4) = log 12.
▸ Quotient Law of Logarithms — The logarithm of a quotient is the difference of the logarithms.
Example: log_a(M/N) = log_a(M) – log_a(N). For example, log 50 – log 5 = log(50/5) = log 10 = 1.
▸ Power Law of Logarithms — The logarithm of a number raised to a power is the power times the logarithm of the number.
Example: log_a(M^k) = k * log_a(M). For example, 3 log 2 = log(2^3) = log 8.
★ Real-world — M-Pesa Growth Orders of Magnitude:
If M-Pesa agent transactions grew from 10,000 to 100,000 per month, the growth factor is 100,000 / 10,000 = 10. Using logarithms, log_10(10) = 1, indicating one order of magnitude growth (a 10-fold increase).
Audio narration — reads aloud, works offline
In your own words, summarise the main idea of this lesson.