Exponential and Logarithmic Equations and Inequalities
Two moves solve everything here: a logarithm frees an unknown trapped in an exponent, and exponentiating frees an unknown trapped inside a log. Multi-log equations condense to a single log first, through the three real properties only, and then convert. The result is a polynomial whose roots are candidates, not answers.
The points are lost after the algebra: candidates that make any original log argument zero or negative are extraneous and must be discarded, even when they satisfy the condensed equation perfectly. Inequalities add the same discipline, carrying the domain wall (x greater than 0, or whatever the argument requires) into the final answer. The lesson drills both the solving and the survivor check.
The work
3 ways in · any order
Lesson
Exponential and Logarithmic Equations and Inequalities
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Logs unlock exponents; exponentials unlock logs; the domain check decides who survives. The lesson walks the condense-convert-check pipeline, plants tempting extraneous roots and defuses them, then closes with ten scenarios of full solves, inequalities, and survivor judgments.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 2.13 misconceptions: condensing with fake sum properties, and keeping extraneous candidates that no original log can accept. The bank ships with the Unit 2 data drop.
Targeted Practice
Drill a single misconception
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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.