Log rules (AA SL 1.7, AI HL 1.9)

Keywords

English	Japanese	Korean	Chinese Simplified
Logarithmic Rules	対数法則	로그 규칙	对数规则
Base Change Rule	底の変換規則	밑변환 법칙	底数变换规则
Simplifying Expressions	式の簡素化	표현식 단순화	简化表达式
Exponential Equations	指数方程式	지수 방정식	指数方程
Logarithmic Equations	対数方程式	로그 방정식	对数方程
Indices Rules	指数法則	지수 규칙	指数规则
Natural Logarithm, ln	自然対数	자연로그	自然对数

Inquiry questions

Factual Inquiry Questions

What are the basic logarithmic rules, including the product, quotient, and power rules?
How can logarithmic rules be used to simplify expressions involving logarithms?

Conceptual Inquiry Questions

Why do logarithmic rules work, and how do they relate to the properties of exponents?
How can understanding logarithmic rules aid in solving exponential and logarithmic equations?

Debatable Inquiry Questions

Is the emphasis on learning logarithmic rules in high school mathematics justified by their application in higher mathematics and real-world problems?
Can the principles behind logarithmic rules be extended to simplify complex problems in fields such as information theory and computational complexity?

Mini-Investigation: Discovering Logarithmic Rules Objective: Use the interactive applet provided to explore and uncover the fundamental rules of logarithms. This investigation will guide you through a series of steps to understand how logarithms work and how their properties are applied. Investigation Steps: Step 1: Discovering the Product Rule - Use the applet to calculate the log of two numbers multiplied together (e.g.,

). - Next, calculate the log of each number separately (log(2) and log(3)) and then add these values together. - Compare the results. What do you notice? This observation will lead you to the Product Rule of logarithms. Step 2: Investigating the Quotient Rule - Repeat a similar process as in Step 2, but this time use division. Calculate the log of a number divided by another (e.g.,

). - Calculate the log of the numerator and the denominator separately (

and

) and then subtract the denominator's log from the numerator's log. - Observe and note the relationship between these values, leading you to the Quotient Rule of logarithms. Step 3: Uncovering the Power Rule - Use the applet to calculate the log of a number raised to a power (e.g.,

). - Calculate the log of the base number (

) and then multiply it by the exponent (

). - Examine how the calculated log compares to the log of the number raised to a power. This will help you understand the Power Rule of logarithms. Step 4: Confirming the Base Change Rule - Experiment with changing the base of the logarithm in the applet. - Try to express a logarithm of one base in terms of logarithms of another base using the applet's outputs. Conclusion: - Summarize the rules you discovered: Product Rule, Quotient Rule, Power Rule, and the Base Change Rule. - Reflect on how these rules help in simplifying complex logarithmic expressions and in solving logarithmic equations.

Checking understanding of simplifying log expressions

Alternatively these more bite-size videos give worked examples of test style questions. Indices rules - This is basic but incredibly important skill that is used later in calculus https://youtu.be/TOXhuEoEi44, Exponentials - Exponential equations (hidden quadratic) , https://youtu.be/12BD5yk4zso , Logarithms https://youtu.be/C2f5NvtMCoU , Natural log - ln(x) , https://youtu.be/dl7mOHtOKu4 Using logs to find unknown powers , https://youtu.be/7sBzT9XdDdo

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