Florida B.E.S.T. MA.912.NSO.1.7
The Standard
Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite logarithmic expressions by applying the product, quotient, and power properties. They also use the inverse relationship between logarithms and exponents while keeping bases and domain restrictions consistent.
What Mastery Looks Like
- Students can expand and condense logarithmic expressions accurately using product, quotient, and power properties. They can name the property used, preserve the base, and state needed input restrictions.
Common Misconceptions
- Students often claim that log(a + b) equals log(a) + log(b), even though no property allows splitting a sum. They may lose the subtraction sign in a quotient or mishandle an exponent when moving it in front. They may also ignore base consistency and restrictions requiring logarithm inputs to be positive.
How to Assess It
- Give an exit ticket: Assume x, y, and z are positive. Expand log₃(x²y/z), then condense 2ln(a) − ½ln(b) into one logarithm.
Lesson moves
Ways to Teach It
Give pairs expression cards and equivalent-form cards to match, then have them label the logarithm property used for each pair.
Ask students to explain why log(x + y) cannot be rewritten as log(x) + log(y), using a numerical counterexample.
Run a relay where teams expand or condense one logarithmic expression, check the previous answer, and pass the next card.
Use the earthquake formula log(A/A₀), and have students rewrite it as a difference of logarithms to compare two measured amplitudes.
Free download
Printable MA.912.NSO.1.7 Worksheet
A ready-to-print activity worksheet aligned to MA.912.NSO.1.7, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- MA.912.NSO.1.3
Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents.
- MA.912.NSO.1.6
Given a numerical logarithmic expression, evaluate and generate equivalent numerical expressions using the properties of logarithms or exponents.
- MA.912.NSO.1.2
Generate equivalent algebraic expressions using the properties of exponents.
- MA.912.NSO.1
Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.