ACT-Style: Logarithm Properties

ACT Math · Axiom Academy

EXAMPLE ACT-Style: Logarithm Properties Combining the product and quotient rules the way it actually shows up on the test Simplify the expression to a single number. Every log property here has a partner operation it's often confused with — mixing them up is exactly how the wrong answer choices get built. Product rule: — the arguments MULTIPLY, they never add. , not . Quotient rule: — the SECOND argument goes on the bottom, not the top. , not . Evaluating a log: asks "2 to what power gives 4?" — the answer is the EXPONENT, not the argument itself. 2^2 = 4 , so , not 4 and not 16 . On the ACT, log-property problems are rarely wrong because of arithmetic — they're wrong because a product-rule step got treated like addition of arguments, or a quotient-rule step got flipped or treated like subtraction of arguments. Naming which rule applies, and which argument goes where, is the real skill.

This is the written version of the interactive lesson above. See the full ACT Math course.