Using Logarithms to Solve Equations

The video tutorial explains how to use logarithms to solve equations where the variable is a power. It covers two main methods: using the log base method and taking logs of both sides. The tutorial provides examples of each method, including solving complex equations. It concludes with a summary of the methods and key concepts, emphasizing the importance of understanding logarithmic laws and using calculators effectively.

What is the primary difference between the equations discussed in this tutorial and normal equations?

• The variable is in the base.

• The equations are linear.

• The variable is in the exponent.

• The equations are quadratic.

In the first method, what is the role of the log base function on a calculator?

• To convert a logarithm to a natural log.

• To calculate the power of a number.

• To find the base of the logarithm.

• To solve for the exponent in an equation.

When using the first method, what is the result of log base 3 of 2187?

• 6

• 5

• 8

• 7

What is the key step in the second method of solving equations using logarithms?

• Subtracting the logs of both sides.

• Multiplying both sides by the base.

• Taking the log of both sides.

• Adding the logs of both sides.

In the second method, what do you do after taking the log of both sides?

• Multiply the logs together.

• Divide one log by the other.

• Subtract one log from the other.

• Add the logs together.

How do you handle equations with variables on both sides using logarithms?

• Use a combination of both methods.

• Use the first method only.

• Use the second method only.

• Use neither method.

What is the result of solving the equation 3^(2x + 1) = 80 using logarithms?

• x = 3.49

• x = 4.49

• x = 2.49

• x = 1.49

What is the final value of x in the equation 7^(x - 3) = 4^(2x)?

• x = -4.06

• x = -5.06

• x = -6.06

• x = -7.06

What is the solution to the equation log base 2 of (x^2 + 4) = 2 + log base 2 of x?

• x = 4

• x = 1

• x = 2

• x = 3

Which law of logarithms allows you to rewrite a subtraction of logs as a division?

• Change of Base Formula

• Power Law

• Quotient Law

• Product Law