Logarithm Properties and Base Change

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Objective

I can use the properties of logarithms to rewrite expressions and apply the change of base formula to evaluate logarithms including natural logs. I can find exact values for logs without calculators

Part 1 of 4

Warm-up video

Professor Dave Explains · 7:06Vetted channel

We don't generate video — this one is by Professor Dave Explains on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.

Part 2 of 4

Key concepts

3 concepts

  1. 1

    If the base of the log and the number that the log operates on are the same, the result will be one, because anything to the first power equals itself, but if we are taking the log of one, the result will always be zero, regardless of the base.

  2. 2

    Logarithms are essentially exponents, so log of AB equals log of A plus log of B, and log of A/B equals log of A minus log of B.

  3. 3

    The three ways to expand logarithmic expressions are the product rule, the quotient rule, and the power rule.

Part 3 of 4

Practice

3 questions

1

Using the properties of logarithms, expand the expression: log(5x² / y)

2

Condense the following expression into a single logarithm: 3log(x) + log(2) - log(y)

Part 4 of 4

Exit ticket

Quick comprehension check

Simplify the expression: log₃(9x²) - log₃(x)

Sample answer included in the free materials

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Teacher guide, student handout, and slides — free, in Google Docs format

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