Logarithmic and Exponential Equations

The video tutorial explains how to solve the equation 3x = log base 6 of 216 by converting the logarithmic expression into exponential form. It demonstrates the process of rewriting the equation to have the same base, allowing the exponents to be equated. The tutorial provides an example of converting a logarithm to exponential form and concludes with solving for x, resulting in x equals one.

What is the initial equation given in the problem?

• 3x = log base 5 of 216

• x = log base 5 of 216

• 3x = log base 6 of 216

• x = log base 6 of 216

What is the base of the logarithm in the initial problem?

• 2

• 10

• 6

• 5

What is the first step in solving a logarithmic equation?

• Graph the equation

• Convert it to a quadratic equation

• Convert it to exponential form

• Solve it directly

In the example given, what is log base 5 of 25 equal to?

• 4

• 3

• 2

• 1

What does the logarithm log base 5 of 25 represent in exponential form?

• 5^4 = 25

• 5^3 = 25

• 5^2 = 25

• 5^1 = 25

What is the exponential form of log base 5 of 25?

• 5^3 = 25

• 5^2 = 25

• 5^1 = 25

• 5^4 = 25

How is the equation 3x = log base 6 of 216 rewritten in exponential form?

• 6^x = 216

• x^6 = 216

• 6^3x = 216

• 3^6x = 216

What is the result of converting log base 6 of 216 to exponential form?

• 6^4x = 216

• 6^3x = 216

• 6^x = 216

• 6^2x = 216

What is the purpose of rewriting logarithmic equations in exponential form?

• To convert to a quadratic equation

• To make them easier to graph

• To simplify the equation

• To solve for the variable

What is the main goal when solving exponential equations?

• To graph the equation

• To simplify the equation

• To equate the bases

• To find the logarithm