Law of Logarithms

Laws of Logarithms

Logarithmic Principle: Understand that the logarithm is the reversal of exponentiation.
Base of Logarithms: Calculate logarithms with bases other than 10 or e. Remember the change of base rule: log_b(a) = log_c(a) / log_c(b).
Product Rule: Recognize the product rule of logarithms which states: log_b(MN) = log_b(M) + log_b(N). This rule is used when you are multiplying terms with the same base.
Quotient Rule: Apply the quotient rule: log_b(M/N) = log_b(M) - log_b(N). This applies when you divide terms with the same base.
Power Rule: Utilize the power rule: log_b(M^n) = n * log_b(M). This applies when a term with a base is raised to a power.
Logarithms of Powers: Know how to calculate logarithms of powers, using the rule log_b(a^n) = n * log_b(a).

Know that when you have an equation in the form log_b(M) = log_b(N), you can drop the logarithms, resulting in M = N.
Understand that logarithms can be converted to exponential form to solve the equation.
Use properties of logarithms to condense or expand the equation, making it easier to solve.
Change of Base Rule: Know how to convert from one base to another to solve logarithmic equations, using the rule: log_b(a) = log_c(a) / log_c(b), where c is the new base.

Understand how logarithms can be used to solve exponential equations.
Be aware of real-life applications such as calculating earthquake intensity using the Richter scale, computing sound intensity using decibels, and modelling population growth or decay in biology.
Understand how logarithmic scales can be used to represent data that covers a large range of values in a more digestible format.