Solving Exponential Equations with Change of Base and DESMOS

The video tutorial introduces solving exponential equations using the change of base method. It begins with basic examples, demonstrating how to equate exponents when bases are the same. The tutorial progresses to using the Desmos graphing calculator to find solutions graphically by identifying points of intersection. Advanced examples are provided, and solutions are verified both algebraically and graphically. The tutorial concludes with a final example, reinforcing the concepts taught.

What is 5 to the third power equal to?

• 25

• 150

• 125

• 15

If 5^x = 5, what is the value of x?

• 1

• 5

• 0

• 3

For the equation 2^(x+7) = 8, what is the value of x after simplifying?

• 3

• 4

• -3

• -4

How do you type the equation 2^(x+7) in Desmos?

• 2x^7

• 2(x+7)

• 2^(x+7)

• 2x+7

What is the base change required to solve the equation 4^(x-5) = 16?

• 4 to the power of 4

• 2 to the power of 2

• 2 to the power of 4

• 4 to the power of 2

What is the value of x in the equation 4^(x-5) = 16?

• 5

• 7

• 3

• 2

In the equation 6^(-x) = 216, what is the correct transformation for 216?

• 6^3

• 6^2

• 2^3

• 3^2

What is the value of x in 6^(-x) = 216?

• -3

• 2

• 3

• -2

For the equation 7^(2x) = 343, what is the simplified form of 343?

• 7^5

• 7^3

• 7^2

• 7^4

What is the value of x in the equation 7^(2x) = 343?

• 3

• 2

• 1.5

• 2.5