Evaluate logarithms using properties

Learning Objectives Apply the product, quotient, and power rules to expand and condense logarithmic expressions. Evaluate logarithmic expressions without a calculator by rewriting them using properties. Use the change of base formula to evaluate logarithms with any base, given known values or a calculator. Simplify complex logarithmic expressions involving multiple properties in a single problem. Recognize and apply the inverse properties of logarithms and exponents to simplify expressions. Differentiate between correct and incorrect applications of logarithm properties to avoid common errors. Ever wonder how scientists measure earthquake intensity or sound levels? 🤯 It all comes down to the power of logarithms! This tutorial will equip you with the essential properties of...

TermDefinitionExample LogarithmThe exponent to which a specified base must be raised to obtain a given number. The expression `log_b(x) = y` is equivalent to the exponential form `b^y = x`.`log_2(8) = 3` because `2^3 = 8`. BaseThe number being raised to a power in an exponential expression, or the subscript number in a logarithm.In `log_5(25)`, the base is 5. ArgumentThe value or expression inside the logarithm on which the function is operating.In `log_3(9x)`, the argument is `9x`. Common LogarithmA logarithm with a base of 10. If no base is written, it is assumed to be 10.`log(1000)` is equivalent to `log_10(1000)`, which equals 3. Natural LogarithmA logarithm with a base of Euler's number, `e` (approximately 2.718). It is written as `ln(x)`.`ln(e^2)` is equivalent to `log_e(e^2)`,...

Product Rule `log_b(M * N) = log_b(M) + log_b(N)` The logarithm of a product is the sum of the logarithms of its factors. This rule is used to expand a single log into a sum or condense a sum into a single log. The bases must be the same. 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. This rule is used to expand a single log into a difference or condense a difference into a single log. The bases must be the same. Power Rule `log_b(M^p) = p * log_b(M)` The logarithm of a number raised to a power is the power multiplied by the logarithm of the number. This allows you to move an exponent from the argument to become a coefficient. Change of Base Formula `log_b(...