LogarithmsLogarithmsYear 11 Maths Extension

LogarithmsLogarithms

ExamplesExamples

AnswersAnswers

What Similarity Can you see What Similarity Can you see in the Next slide to do with in the Next slide to do with the Logarithm Laws?the Logarithm Laws?

Logarithm LawsLogarithm Laws

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Logarithm LawsLogarithm LawsThe index laws can be used to

establish corresponding rules for calculations involving logarithms.

It is important to remember that each rule works only if the base, a, is the same for each term.

Solve The following Solve The following Questions (“,)Questions (“,)

AnswersAnswers

SolveSolve

AnswerAnswer

SolveSolve

Answer (a)Answer (a)

Answer (b)Answer (b)

Answer (c)Answer (c)

CALCULATOR TIME!!!!CALCULATOR TIME!!!!

Logarithms to the base 10Logarithms to the base 10

Solving logarithmic Solving logarithmic equationsequations

ExamplesExamples

ExamplesExamples

ExamplesExamples

ExamplesExamples

Points to Remember!!!!Points to Remember!!!!

logarithmic graphslogarithmic graphs

Note your Rules!!!!Note your Rules!!!!A > 0 and m, n > 0A > 0 and m, n > 0

Plotting logarithmic Plotting logarithmic graphsgraphs steps for plotting this

graph:

xy 10log

xay yLogTheOfInversex 10...

y 10y x x , y-1 10-1 1/10 (1/10 , -1)

0 100 1 (1 , 0)

1 101 10 (10 , 1)

Plotting logarithmic Plotting logarithmic graphsgraphs

y 10y x x , y-1 10-1 1/10 (1/10 , -1)

0 100 1 (1 , 0)

1 101 10 (10 , 1)

ExampleExampley 2y x x , y-1 2-1 1/2 (1/2 , -1)

0 20 1 (1 , 0)

1 21 2 (2 , 1)

2 22 4 (4 , 2)