Solving Advanced Exponential Equations

The video tutorial provides practice in solving exponential equations. It begins with an introduction to the topic, followed by a detailed, step-by-step solution of two different exponential equations. The first equation involves rewriting numbers as powers of 2, while the second equation involves rational expressions and powers of 5. The tutorial emphasizes finding common bases and simplifying exponents to solve for x.

What is the first step in solving exponential equations with different bases?

• Subtract the exponents

• Divide the exponents

• Find a common base

• Add the exponents

What is 32 expressed as a power of 2?

• 2^6

• 2^3

• 2^4

• 2^5

How can you simplify (2^5)^(x/3)?

• 2^(3x/5)

• 2^(5x/3)

• 2^(5/x)

• 2^(x/15)

What is the simplified form of 2^(3x-36)?

• 2^(x-36)

• 2^(3x-12)

• 2^(3x-36)

• 2^(x-12)

What is the value of x when 5x/3 = 3x - 36?

• x = 18

• x = 12

• x = 27

• x = 36

How can 25 be expressed in terms of 5?

• 5^3

• 5^4

• 5^2

• 5^1

What is the simplified form of (5^2)^(9-x)?

• 5^(18-2x)

• 5^(9-x)

• 5^(9-2x)

• 5^(18-x)

What is the next step after simplifying the left-hand side of the equation 5^(4x+3) / 5^(18-2x)?

• Divide the exponents

• Subtract the exponents

• Multiply the exponents

• Add the exponents

What is the simplified form of 4x + 3 - (18 - 2x)?

• 2x - 15

• 6x - 15

• 6x - 21

• 4x - 15

What is the value of x when 4x - 20 = 0?

• x = 4

• x = 6

• x = 7

• x = 5