Topicm79e87823ec0bab54_1528449000663_0Topic

LogarithmlogarithmLogarithm operations. Logarithm of the quotient

Levelm79e87823ec0bab54_1528449084556_0Level

Third

Core curriculumm79e87823ec0bab54_1528449076687_0Core curriculum

I. Real numbers. The student:

1) performs operations (addition, subtraction, multiplication, division, exponentiation, square rooting, logarithms) in the set of real numbers;

9) uses the logarithmic relationship with exponentiation, uses the logarithmlogarithmlogarithm of the product, the logarithm of the quotient and the logarithm of powerpowerpower.

Timingm79e87823ec0bab54_1528449068082_0Timing

45 minutes

General objectivem79e87823ec0bab54_1528449523725_0General objective

Interpreting and manipulating information presented in the text, both mathematical and popular science, as well as in the form of graphs, diagrams, tables.

Specific objectivesm79e87823ec0bab54_1528449552113_0Specific objectives

1) Communicating in English, developing mathematics, scientific, technical and IT competences, developing learning skills.

2) Understanding the properties of operations on logarithms - the logarithmlogarithmlogarithm of the quotient.

3) Applying the formula for the logarithmlogarithmlogarithm of the quotient.

Learning outcomesm79e87823ec0bab54_1528450430307_0Learning outcomes

The student:

- learns the properties of operations on logarithms - the logarithmlogarithmlogarithm of the quotient,

- uses the formula for the logarithmlogarithmlogarithm of the quotient.

Methodsm79e87823ec0bab54_1528449534267_0Methods

1) Diamond ranking.

2) Situational analysis.

Forms of workm79e87823ec0bab54_1528449514617_0Forms of work

1) Individual work.

2) Group work.

Lesson stages

Introductionm79e87823ec0bab54_1528450127855_0Introduction

Students revise their current knowledge about logarithms working according to the diamond ranking method.

Procedurem79e87823ec0bab54_1528446435040_0Procedure

The teacher informs students that the aim of the lesson is to learn and use the formula for the logarithmlogarithmlogarithm quotient rule in the calculations.

Students, working in groups, using computers, analyze the animation presenting the formula for the logarithm of the quotient and its proof. They write the appropriate theorem.

[Slideshow]

Students note down the theorem - the logarithm of the quotient.

With the positive and different from 1 base a of the logarithm, for any positive numbers x > 0 and y > 0, the following equality is truem79e87823ec0bab54_1527752263647_0With the positive and different from 1 base a of the logarithm, for any positive numbers x > 0 and y > 0, the following equality is true

Task
Rewrite as a single term.

a) ${\log }_{4}3-{\log }_{4}6$

b) ${\log }_{3}18-{\log }_{3}9$

c) $3-{\log }_{2}5$

d) ${\log }_{0,5}5-{\log }_{0,5}4$

Task
Calculate the value of the term.

a) ${\log }_{9}27-{\log }_{9}729$

b) ${\log }_{9}48-{\log }_{2}3+{\log }_{2}32$

c) ${\log }_{5}2-{\log }_{5}250$

d) ${\log }_{0,5}7-{\log }_{0,5}56$

Task
Calculate the value of the term.

a) ${\log }_{10}2\sqrt{5}-{\log }_{10}\sqrt{5}$

b) ${\log }_{7}63-{\log }_{7}9$

c) ${\log }_{10}500-{\log }_{10}50$

d) ${\log }_{3}72-{\log }_{3}8$

Task
Check if the following equalities are true.

a) ${\log }_{2}6={\log }_{2}48-3$

b) ${\log }_{10}7={\log }_{10}70-1$

Task
The logarithm with base 10, is called the decimal logarithm or the decadic logarithm. We writem79e87823ec0bab54_1527752256679_0The logarithm with base 10, is called the decimal logarithm or the decadic logarithm. We write ${\log }_{10}x$ or $logx$.

Calculate

a) ${\log }_2\left(\log 100000\right)$

b) ${\log }_2\left({\log }_{3}2187\right)$

Task
Proof that log200 is a number less than 3.

Task for volunteers
Knowing that $\log \mathrm{7\approx 0,8}$ and $\log 4\approx 0,6$ calculate the approximate value of the term

a) $\log \frac{4}{7}$

b) $\log 1\frac{3}{4}$

Lesson summarym79e87823ec0bab54_1528450119332_0Lesson summary

Students do the revision exercises. Together, they formulate the theorem to remember.

- With the positive and different from 1 base a of the logarithmlogarithmlogarithm, for any positive numbers x and y, the following equality is true

Selected words and expressions used in the lesson plan

algorithm of quotientalgorithm of quotientalgorithm of quotient

argument of logarithmargument of logarithmargument of logarithm

base of logarithmbase of logarithmbase of logarithm

decadic / decimallogarithmdecadic / decimal logarithmdecadic / decimallogarithm

difference of logarithms with the same basedifference of logarithms with the same basedifference of logarithms with the same base

exponentexponentexponent

logarithmlogarithmlogarithm

powerpowerpower