Logarithmic Equations and Solutions

The video tutorial explains how to solve logarithmic equations by isolating the logarithm and converting it into an exponential equation. It provides three examples: solving log base 5 of X, solving log base X of 32 using prime factorization, and solving when the variable is outside the logarithm. The tutorial emphasizes understanding the relationship between logarithms and exponents and offers alternative methods for solving equations.

What is the first step in solving a logarithmic equation?

• Add the base to both sides

• Multiply both sides by the base

• Isolate the logarithm

• Convert it to a quadratic equation

In the first example, what is the base of the logarithm?

• X

• 10

• 5

• 2

What is the solution for X in the first example?

• 10

• 15

• 25

• 30

In the second example, what is the base of the logarithm?

• X

• 10

• 32

• 5

What is the prime factorization of 32 used in the second example?

• 2^4

• 5^2

• 2^5

• 3^5

What is the solution for X in the second example?

• 1

• 4

• 3

• 2

In the third example, what is unique about the variable X?

• It is the number in the logarithm

• It is not part of the logarithm

• It is the exponent of the logarithm

• It is the base of the logarithm

What is the solution for X in the third example?

• 3

• 1

• 0

• 2

What alternative method is shown in the third example?

• Graphing the equation

• Evaluating the logarithm first

• Using the quadratic formula

• Using a calculator

What can be used if the logarithm does not evaluate to a nice value?

• Substitution method

• Graphing method

• Quadratic formula

• Change of base formula