[list][*]Subject: [b] Mathematics[/b][br][/*][*]Grade Level: [b]10[/b]th grade[/*][*]Duration: about [i]50 min [/i][/*][*]Technology setting:[i] Computer and projector [/i][i]for teacher, computers/ tablets for students.[/i][/*][/list]

[b]Logarithmic function. Properties.[/b][br]The geometric representation of the graph of the logarithmic base function supraunitary and subunitary, identification of its inversion by right symmetry y = x (first bisector), solving some equations.[br]

[i]During the lesson, students:[/i] [list][*] will discover the graph of the logarithmic function with a supraunit and subunit base;[br][/*][*] will see, through graphical reading, the properties of the functions: monotony, convexity, infinite variation (slope) ...[br][/*][*] will explore the sign of the logarithmic function;[br][/*][*] will identify the exponential function as the inverse logarithmic function.[/*][/list][i][i]After the lesson,[/i]students will know :[br][/i][list][*][i] [/i] the properties of the logarithmic function in relation to the base;[br][/*][*] students will know how to compare the logarithm of the same number in relation to the base;[/*][*] that the logarithmic function is inverse to the exponential function.[/*][/list][i]As a result of the lesson,students will be able to do it :[/i][br][list][*]to plot the logarithmic function graph;[/*][*]to compare two logarithms;[/*][*]to resolve some of the equations graphically.[br][/*][/list]

[b]Lesson objectives:[/b][list][*]students can draw through points the graph of the logarithmic function;[br][/*][*]students can explain the properties of the logarithmic function;[br][/*][*]in relation to the base, can distinguish the differences between properties;[br][/*][*]identifies the inverse logarithmic function;[br][/*][*]can explain inequalities between logarithms;[br][/*][*]can read from the graph the sign of the logarithmic function.[/*][/list][b]Assessment: [/b][list][*]check the students' written notes;[br][/*][*]in applet 2, changing the logarithm base, students are required to observe the properties and list them;[br][/*][*]discussions about the power of infinite convergence of the logarithm with the help of the tangent slope to the graph.[br][/*][/list][b]Prior Knowledge:[/b][br][list][*]students need to be familiar with identifying the properties of a graphical reading function;[br][/*][*]students need to know the graph of the exponential function;[br][/*][*]students need to know the relationship between the function graphs [math]f[/math] and [math]f^{-1}[/math].[/*][/list]

[i]Methods and strategies:[/i][i][br][list][*]learning by discovery;[br][/*][*]questioning;[br][/*][*]conversation, observation.[br][/*][/list]Equipment:[br][list][*][i]Computer and projector [/i][i]for teacher;[/i][/*][*][i]computers/ tablets for students.[/i][/*][/list][/i]

[list][*][i] [/i]Students need to be familiar with identifying the properties of a graphical reading function; to know the graph of the exponential function; to know the relationship between the function graphs [math]f[/math] and [math]f^{-1}[/math].[br][/*][*]In order to have no problems, before the lesson I will ensure that all pupils have their applets downloaded on their equipment.[br][/*][/list]