Logarithmic and Exponential Equations

The video tutorial explains how to solve a logarithmic equation by isolating the logarithm, converting it to an exponential form, and solving for the variable X. The process involves dividing both sides of the equation to isolate the logarithm, rewriting the equation in exponential form, and then solving for X by performing arithmetic operations. The tutorial provides step-by-step instructions and demonstrates two methods for entering equations using a keyboard or a math palette. The final solution to the equation is X = 212.

What is the first step in solving a logarithmic equation with a single log?

• Subtract the base from both sides

• Add a constant to both sides

• Isolate the logarithm

• Multiply both sides by the base

How do you isolate the logarithm in the equation 3 x log base 6 of (x + 4) = 9?

• Subtract 3 from both sides

• Divide both sides by 3

• Add 3 to both sides

• Multiply both sides by 3

Which of the following is a method to enter the isolated logarithmic equation?

• Using a calculator

• Using a math pallet

• Typing directly into a text editor

• Drawing it on paper

What is the exponential form of the equation log base 6 of (x + 4) = 3?

• x + 4 = 3^6

• x + 4 = 6^3

• x + 4 = 6^6

• x + 4 = 3^3

What is the purpose of converting a logarithmic equation to an exponential form?

• To simplify the equation

• To solve for the base

• To solve for the exponent

• To solve for the variable

What is the base in the logarithmic equation log base 6 of (x + 4) = 3?

• x + 4

• 9

• 6

• 3

What is the value of 6 raised to the power of 3?

• 36

• 18

• 216

• 1296

What is the final step to find the exact solution for x in the equation x + 4 = 216?

• Add 4 to both sides

• Multiply both sides by 4

• Divide both sides by 4

• Subtract 4 from both sides

What is the exact solution for x in the equation x + 4 = 216?

• x = 220

• x = 212

• x = 210

• x = 214

Which operation is used to solve for x after converting the equation to exponential form?

• Division

• Addition

• Subtraction

• Multiplication