Understanding Logarithms and Exponential Equations

The video tutorial explains how to solve a logarithmic equation using the change of base formula and the power property of logarithms. It begins by rewriting the equation with a common base, then applies the power property to simplify the expression. The tutorial continues by simplifying the equation further, leading to a final solution where the logarithmic equation is converted into an exponential form, resulting in the solution x equals four.

What is the purpose of using the change of base formula in the given problem?

• To convert the logarithm to a different base for easier calculation

• To eliminate the logarithm entirely

• To solve the equation directly

• To change the equation into a polynomial

Which property of logarithms allows us to move the exponent to the front of the logarithm?

• Product Property

• Quotient Property

• Power Property

• Change of Base Property

What is the result of simplifying 2 divided by 2 in the context of the problem?

• Zero

• Four

• Two

• One

After applying the power property, what is the simplified form of the expression?

• log base 2 of x squared equals 4

• 2 log base 2 of x equals 4

• log base 2 of 4 equals x

• log base 2 of x equals 4

How do you express the logarithmic equation log base 2 of x equals 2 in exponential form?

• x equals 2 plus 2

• x equals 2 squared

• x equals 2 to the power of 2

• x equals 2 times 2

What is the final solution for x in the equation?

• x equals 4

• x equals 2

• x equals 8

• x equals 16