Exponential Functions and Logarithms

The video tutorial explains how to solve a logarithmic equation by first isolating the logarithm and then converting it into an exponential equation. It provides methods for entering the equation into a system and calculating both the exact solution and its decimal approximation. The tutorial emphasizes the importance of using the correct symbols and rounding rules in calculations.

What is the first step in solving the equation 4 x log base 5 of x = 3?

• Divide both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides

• Multiply both sides by 4

How can you enter the isolated logarithm equation using a keyboard?

• LOG_5(X = 3/4)

• LOG_5(X = 4/3)

• LOG_5(X) = 3/4

• LOG_5(X) = 4/3

What is the next step after isolating the logarithm in the equation?

• Graph the equation

• Solve for y

• Convert it to an exponential equation

• Convert it to a linear equation

What is the base in the exponential equation derived from log base 5 of x = 3/4?

• 3

• 4

• 5

• x

What is the exponential form of the equation log base 5 of x = 3/4?

• x = 3/4^5

• x = 5^(3/4)

• x = 4/3^5

• x = 5^3

How can you enter the exponential equation using a keyboard?

• 5^3/4

• 5^(3/4)

• 5^(4/3)

• 5^4/3

What is the exact solution for x in the equation x = 5^(3/4)?

• x = 3/4^5

• x = 5^(3/4)

• x = 5^3

• x = 4/3^5

What is the decimal approximation of 5^(3/4) to three decimal places?

• 3.343

• 3.345

• 3.346

• 3.344

Why is it important to use the equal sign instead of an approximation symbol in the homework system?

• To simplify the equation

• To show a rounded solution

• To indicate an exact solution

• To avoid errors

What does the 7 in the fourth decimal place indicate when rounding 5^(3/4)?

• Round down

• Round up

• Keep the same

• Ignore it