Understanding Logarithmic and Exponential Equations

The video tutorial explains how to solve logarithmic equations by converting them into exponential form. It covers the basic definition of logarithms and provides four examples demonstrating different scenarios, including solving equations with different bases, negative exponents, and using prime factorization. The tutorial aims to help viewers understand the relationship between logarithms and exponents and how to manipulate these equations to find solutions.

What is the equivalent exponential form of log base b of n equals a?

• a raised to the power of b equals n

• n raised to the power of b equals a

• b raised to the power of a equals n

• b raised to the power of n equals a

In the first example, what is the value of x if 4^x = 64?

• x = 4

• x = 5

• x = 2

• x = 3

How can 64 be expressed as a power of 4?

• 4^2

• 4^5

• 4^3

• 4^4

In the second example, what is the value of x if 2^x = 1/16?

• x = -3

• x = -5

• x = -2

• x = -4

How can 1/16 be expressed as a power of 2?

• 2^-4

• 2^-3

• 2^-2

• 2^-5

In the third example, what is the value of x if log base 5 of x equals 3?

• x = 15

• x = 25

• x = 125

• x = 225

What is 5 raised to the power of 3?

• 100

• 75

• 25

• 125

In the final example, what is the value of x if x^4 = 81?

• x = 4

• x = 3

• x = 5

• x = 2

How can 81 be expressed as a power of 3?

• 3^2

• 3^3

• 3^4

• 3^5

What is the prime factorization of 81?

• 3 x 3 x 3

• 9 x 9

• 3 x 9

• 3 x 3 x 3 x 3