Understanding Logarithmic and Exponential Equations

The video tutorial explains how to solve logarithmic equations by converting them into exponential equations. It demonstrates two examples: the first involves solving for x using cube roots and prime factorization, while the second uses fifth roots and rational exponents. The tutorial provides both exact solutions and decimal approximations, ensuring the simplification process is correct.

What is the first step in solving a logarithmic equation?

• Integrate the equation

• Find the derivative

• Convert it to an exponential equation

• Convert it to a quadratic equation

In the first example, what is the base of the exponential equation?

• Two

• Three

• Five

• Four

How many factors of two are there in the prime factorization of four to the fifth?

• Five

• Seven

• Ten

• Twelve

What is the exact value of x in the first example?

• Four times the cube root of 2

• Eight times the cube root of 2

• Four times the square root of 2

• Eight times the square root of 2

What is the decimal approximation of x in the first example?

• 9.0794

• 10.0794

• 8.0794

• 11.0794

What mathematical operation is used to verify the solution in the first example?

• Cube root calculation

• Subtraction

• Addition

• Multiplication

In the second example, what is the exponent of three in the equation?

• Negative five

• Positive five

• Negative four

• Positive four

What is the simplified form of three to the negative fourth power?

• Three to the fourth

• One over three to the fifth

• One over three to the fourth

• Three to the negative fifth

What is the exact value of x in the second example?

• One divided by the fourth root of 81

• One divided by the square root of 81

• One divided by the fifth root of 81

• One divided by the cube root of 81

What is the decimal approximation of x in the second example?

• 0.6152

• 0.5152

• 0.4152

• 0.3152