Solving Exponential and Logarithmic Equations

The video tutorial explains how to solve exponential equations by converting them into logarithmic equations and using the change of base formula. It demonstrates solving two equations: 5^x = 476 and 3^x = 246, using natural logarithms and a calculator. The tutorial concludes with a brief mention of solving similar equations using logarithmic properties in future videos.

What is the first step in solving an exponential equation using logarithms?

• Convert the equation to a quadratic form

• Write the equation as a logarithmic equation

• Multiply both sides by the base

• Add the base to both sides

What does the change of base formula allow you to do?

• Solve quadratic equations

• Find the derivative of a logarithmic function

• Evaluate any logarithm using a calculator

• Convert logarithms to exponential form

Tags

CCSS.HSF.BF.B.5

In the equation 5^x = 476, what is the base of the logarithm used?

• x

• 476

• 10

• 5

Tags

CCSS.HSF.LE.A.4

What is the approximate value of x when solving 5^x = 476 using natural logs?

• 3.8308

• 4.1234

• 2.3456

• 5.6789

Tags

CCSS.HSF.LE.A.4

What is the first step in solving the equation 3^x = 246?

• Subtract 3 from both sides

• Divide both sides by 4

• Add 4 to both sides

• Multiply both sides by 3

What is the base of the logarithm used in solving 3^x = 246?

• 4

• 246

• 3

• x

Tags

CCSS.HSF.LE.A.4

What is the approximate value of x when solving 3^x = 246 using natural logs?

• 6.1234

• 4.5678

• 5.0112

• 3.4567

What should be the result of 4 x 3^5.0112 according to the solution?

• More than 1000

• Less than 900

• Exactly 1000

• Approximately 984

What will be covered in another video according to the conclusion?

• Using properties of logarithms to solve equations

• Graphing exponential functions

• Calculating derivatives of exponential functions

• Solving equations using the quadratic formula

What is the purpose of verifying the solutions using a calculator?

• To find the exact value of x

• To ensure the solution is approximately correct

• To simplify the equation further

• To change the base of the logarithm