Exponential Equations and Powers

This lesson explores equivalent forms of exponential equations, focusing on expressing numbers as powers with the same base. It covers solving exponential equations using logarithms and changing the base to find solutions. The lesson includes multiple examples to illustrate these concepts, emphasizing the importance of understanding powers and exponents in solving equations.

What is the main focus of the lesson on exponential equations?

• Solving quadratic equations

• Understanding equivalent forms of exponential equations

• Learning about linear equations

• Studying polynomial functions

How can 4 squared be expressed as a power with a base of 2?

• 2 to the power of 4

• 2 to the power of 5

• 2 to the power of 3

• 2 to the power of 2

What power of 2 equals 64?

• 2 to the power of 6

• 2 to the power of 5

• 2 to the power of 7

• 2 to the power of 4

How is 8 expressed as a power of 2?

• 2 to the fifth

• 2 to the fourth

• 2 cubed

• 2 squared

What is the power of 2 that equals 128?

• 2 to the power of 7

• 2 to the power of 6

• 2 to the power of 8

• 2 to the power of 5

How do you find the power of 2 that equals 20 using logarithms?

• By using the square root

• By multiplying exponents

• By dividing by 2

• By converting to logarithmic form

What is the general rule for converting between exponential and logarithmic forms?

• The exponent must be zero

• The base of the power must be different from the base of the logarithm

• The base must be a negative number

• The base of the power and the base of the logarithm must be the same

In Example 2, what common base is used to solve the equation with bases 2 and 4?

• Base 3

• Base 5

• Base 2

• Base 6

How is the solution verified in the example with bases 9 and 27?

• By checking the sum of the exponents

• By using a graphing calculator

• By substituting the solution back into the original equation

• By dividing the bases