Evaluating Exponential Equations and Logarithms

The video tutorial covers solving logarithmic expressions using mental math. It begins with an introduction to logarithms and solving expressions with base 2, emphasizing the concept of zero power. The tutorial then explains common logarithms with base 10, focusing on decimal movement and negative exponents. It proceeds to solve logarithmic expressions with base 4, highlighting the power of 4. Finally, it addresses solving logarithms with decimal bases, demonstrating the use of calculators to find solutions.

What is the main focus of problems 25 through 28?

• Evaluating logarithmic expressions using mental math

• Learning about calculus derivatives

• Solving quadratic equations

• Understanding trigonometric identities

What is the value of x in the equation 2^x = 1?

• -1

• 2

• 0

• 1

What is the base of the common logarithm used in log 0.001?

• 10

• 2

• 5

• e

How many decimal places do you move to convert 0.001 to 1?

• Four

• Three

• Two

• One

What is the value of x in the equation 10^x = 0.001?

• 0

• -1

• -2

• -3

What is the value of 4^x when x equals 3?

• 128

• 16

• 32

• 64

What is the value of x in the equation 4^x = 64?

• 5

• 4

• 3

• 2

What is the base in the equation 0.1^x = 100?

• 0.1

• 1

• 10

• 100

How many times do you move the decimal to convert 0.1 to 100?

• Three

• Two

• Four

• One

What is the value of x in the equation 0.1^x = 100?

• -1

• -4

• -2

• -3