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1.4 Logarithms II
Mathematics · Grade 11 · 8 lessons in the design
What this covers
- Logarithmic notation and its link to index form
- Laws of logarithms: product, quotient, power and roots, derived from the laws of indices
- Simplification of logarithmic expressions; logarithmic equations with unknown arguments, indices and bases
- Applications of the laws of logarithms, including numerical calculations with 4-decimal logs
What you will be able to do
- relate index form to logarithmic notation
- simplify logarithmic expressions using laws of logarithms
- solve logarithmic equations in different situations
- apply laws of logarithms in different situations
- explore the use of logarithms in real life situations
Key questions
“Why are logarithms important?”
Lessons
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From a power to a logarithm
40 min · 1 practice tasks · quizRewrite b to the power c equals a as log base b of a equals c, and reject bases or arguments that make the log undefined.
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Product and quotient laws
40 min · 1 practice tasks · quizDerive log of a product and log of a quotient from the index laws, and show that log of a sum is a different operation.
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Power and root laws
40 min · 1 practice tasks · quizDerive the power law from indices, and use a root as a fractional multiplier in front of the log.
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Simplifying log expressions
40 min · 1 practice tasks · quizCombine sums, differences and powers of the same base into a single log, then evaluate it.
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Logarithmic equations
40 min · 1 practice tasks · quizSolve equations with an unknown inside a log, then reject any root that makes an argument zero or negative.
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Unknown index or unknown base
40 min · 1 practice tasks · quizSolve an exponential equation by matching powers, and solve for a base while keeping the base positive and not equal to 1.
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Calculating with given logs
40 min · 1 practice tasks · quizUse log base 10 of 2 equals 0.3010 and log base 10 of 3 equals 0.4771 to find logs of products, quotients and powers.
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Why the laws are used
40 min · 1 practice tasks · quizFind a doubling time exactly, estimate a less tidy doubling with the given logs, read a power-of-ten pH, and check a change of base.