Logarithmic Expressions
A logarithm answers exactly one question: what exponent turns the base into the argument? Everything in this topic is that sentence applied: converting between log form and exponential form, evaluating logs of perfect powers exactly (including the negative logs of small fractions), and trapping in-between values like log base 3 of 50 between consecutive integer exponents.
The two misconceptions are stubborn. First, the three numbers in a log statement drift out of their roles, so students square the wrong thing or divide argument by base. Second, logs get "distributed" over addition, though no such rule exists: adding logs multiplies arguments, and the log of a sum must be computed by adding first. The lesson names both and drills them to death.
The work
3 ways in · any order
Lesson
Logarithmic Expressions
›
Read every log as the exponent question and this topic collapses into arithmetic. The lesson locks the base-argument-exponent roles, builds exact values for perfect powers and fractions, brackets in-between logs, and detonates the log-of-a-sum myth with numeric counterexamples. Ten scenarios close it out.
Diagnostic
10-item topic check
›
Ten items spanning the two Topic 2.9 misconceptions: base, argument, and exponent trading places in conversions, and log applied over addition as if a sum rule existed. The bank ships with the Unit 2 data drop.
Targeted Practice
Drill a single misconception
›
Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.