Solving Exponential Equations Using Tables and Graphs

The video tutorial demonstrates how to solve the equation 3^x = 57 using both a table and a graph. Initially, it explains that the exact solution cannot be found by expressing 57 as a power of 3, so an approximate solution is sought. The tutorial guides viewers through using a graphing calculator to input the equation and find the solution using a table, adjusting the table settings for precision. It then shows how to graph the equation and a horizontal line to find the intersection point, confirming the solution. The tutorial emphasizes the use of technology and prepares viewers for future lessons on logarithms.

What is the equation we are trying to solve using tables and graphs?

• 3^x = 57

• 2^x = 57

• 3^x = 27

• 2^x = 81

Why can't we find the exact value of x in the equation 3^x = 57?

• Because 57 is not a power of 3

• Because 57 is an even number

• Because 57 is a prime number

• Because 3 is not a factor of 57

What is the initial range of x values considered for the solution?

• Between 1 and 2

• Between 3 and 4

• Between 4 and 5

• Between 2 and 3

What is the first step in using the graphing calculator to solve the equation?

• Enter Y = 57

• Enter Y = 3^x

• Set the window range

• Press the graph button

What change in the table is set to find the solution to one decimal place?

• 0.01

• 0.1

• 0.5

• 1.0

What x value gives a y value closest to 57 in the table?

• 3.6

• 3.9

• 3.5

• 3.7

What is entered as Y2 in the graphing calculator for the graphical solution?

• 57

• 3^x

• x

• 0

What is the purpose of setting up the window in the graphing calculator?

• To save the graph

• To change the color of the graph

• To include the range of x and y values needed

• To adjust the brightness of the screen

What option is selected to find the intersection point on the graph?

• Option 5 for Intersection

• Option 2 for Zero

• Option 3 for Minimum

• Option 1 for Value

What is the approximate solution for x when rounded to one decimal place?

• 3.9

• 3.5

• 3.7

• 3.6