Exponential Equations and Properties

The video tutorial explains how to solve exponential equations with like bases, avoiding the use of logarithms. It covers three examples: using base 6, base 5, and a fraction with negative exponents. The instructor demonstrates how to create factor trees, set exponents equal, and solve for x. The tutorial emphasizes understanding the process of rewriting numbers with like bases and solving equations step-by-step.

What is the base used to solve the exponential equation involving 216?

• 9

• 6

• 12

• 3

How can you determine if a number is divisible by 6?

• None of the above

• The sum of its digits is divisible by 3

• Both A and B

• It ends in an even number

What is the value of x in the equation 6^x = 216?

• 4

• 5

• 3

• 2

In the equation 5^(2x+4) = 25, what is the equivalent expression for 25?

• 5^4

• 5^1

• 5^3

• 5^2

What is the first step in solving 5^(2x+4) = 25?

• Rewrite 25 as 5^2

• Divide both sides by 5

• Set the exponents equal

• Subtract 4 from both sides

What is the value of x in the equation 5^(2x+4) = 25?

• 0

• -1

• 1

• 2

How is the fraction 1/16 expressed as a power of 2?

• 2^2

• 2^-2

• 2^4

• 2^-4

What is the base used to solve the equation involving the fraction 1/16?

• 2

• 4

• 8

• 16

What is the value of x in the equation 2^x = 1/16?

• -3

• -5

• -2

• -4

What is the process to move a fraction's base to the numerator in exponential form?

• Multiply by the base

• Divide by the base

• Add a negative exponent

• Add a positive exponent