Identify properties of logarithms

Learning Objectives State the product, quotient, and power rules for logarithms. Identify which logarithmic property is applicable to a given expression. Apply the properties of logarithms to expand a single logarithmic expression into multiple terms. Apply the properties of logarithms to condense multiple logarithmic terms into a single expression. Use the properties of logarithms to simplify and evaluate logarithmic expressions. Apply the change of base formula to evaluate logarithms with any base. How can we compare the power of an earthquake that measures 7 on the Richter scale to one that measures 5? 🤔 Logarithms hold the key! Just like exponents have rules for multiplication and division, logarithms have their own set of properties. Mastering these properties is the...

TermDefinitionExample LogarithmA logarithm is the exponent to which a specified base must be raised to get a certain number. It is the inverse operation of exponentiation. If b^y = x, then log_b(x) = y.Since 2^3 = 8, the logarithm is log_2(8) = 3. BaseIn the expression log_b(x), 'b' is the base. It is the number that is being raised to a power in the equivalent exponential form.In log_5(25), the base is 5. ArgumentIn the expression log_b(x), 'x' is the argument. It is the number you are taking the logarithm of. The argument must always be a positive number.In log_3(81), the argument is 81. Common LogarithmA logarithm with base 10. It is usually written as log(x) without an explicit base.log(100) is the common log of 100, which equals 2 because 10^2 = 100. Natural Logar...

Product Rule log_b(MN) = log_b(M) + log_b(N) The logarithm of a product is the sum of the logarithms of its factors. Use this to expand a single log with a product in its argument or to condense a sum of logs into a single log. Quotient Rule log_b(M/N) = log_b(M) - log_b(N) The logarithm of a quotient is the difference of the logarithms of the numerator and the denominator. Use this to expand a single log with a fraction in its argument or to condense a difference of logs into a single log. Power Rule log_b(M^p) = p * log_b(M) The logarithm of a number raised to a power is the power times the logarithm of the number. This rule allows you to move an exponent from the argument to become a coefficient in front of the logarithm. Change of Base Formula log_b(M) = lo...