Exploring Logarithmic and Exponential Functions

This video tutorial covers solving logarithmic and exponential functions, starting with basic rules for solving exponential equations by expressing each side as a power of the same base. It progresses to using logarithms to solve exponential equations and then addresses solving logarithmic equations by converting them to exponential form. The tutorial concludes with solving word problems involving exponential growth models, providing practical examples and step-by-step solutions.

What can be done to make the bases of 4 and 2 the same in an equation?

• Cube the base 4

• Square the base 4

• Square the base 2

• None of the above

What mathematical operation is used to make the bases the same in an equation?

• Subtraction

• Addition

• Exponentiation

• Multiplication

What is the result when the bases 64 and 4 are expressed with the same base?

• 64 cubed equals 4

• 4 squared equals 64

• 4 cubed equals 64

• 64 squared equals 4

What is the correct transformation for the base 64 to match base 4?

• 4 to the power of 3

• 64 to the power of 1/3

• 64 to the power of 3

• 4 to the power of 1/3

How do you isolate an exponential expression in an equation?

• Both A and B

• None of the above

• Multiply or divide by the coefficient

• Add or subtract the constant

What logarithmic operation is used to bring down the exponent in the equation 2 to the x equals 7?

• Log base 7

• Natural log

• Log base 2

• Log base 10

Tags

CCSS.HSF.BF.B.5

What is the inverse operation used to solve logarithmic equations?

• Dividing by the base

• Taking the exponent

• Taking the square root

• Multiplying by the base

How is the log base 4 removed from an equation?

• By raising 4 to the power of the log base 4

• By dividing by 4

• By subtracting 4

• By adding 4

In the bacterial reduction problem, what is the initial number of bacteria?

• 7000 bacteria

• 1750 bacteria

• 14000 bacteria

• 3500 bacteria

Tags

CCSS.HSF.LE.A.4

What year is predicted for the population to reach 50,000 according to the exponential growth model?

• 2050

• 2025

• 1990

• 2015

Tags

CCSS.HSF.LE.A.4