Exponential Equations and Properties

The video tutorial explains how to solve exponential equations by ensuring the bases are the same. It covers three examples: rewriting 36 as 6 squared, expressing 64 and 16 as powers of 4, and expressing 81 as a power of 9. An alternate method for solving the second example using powers of 2 is also demonstrated.

What is the key property used to solve exponential equations with the same base?

• The exponents are equal.

• The bases are added.

• The exponents are subtracted.

• The bases are multiplied.

In Example A, what is the exponent of 6 when 36 is rewritten as a power of 6?

• 3

• 1

• 2

• 4

What is the value of x in the equation 6^x = 36?

• 2

• 1

• 4

• 3

In Example B, 64 is rewritten as a power of which number?

• 3

• 2

• 5

• 4

What is the value of x in the equation 4^(3x) = 4^2?

• 2/3

• 1/2

• 3/4

• 1

In Example C, 81 is rewritten as a power of which number?

• 9

• 8

• 10

• 7

What is the value of x in the equation 9^(2x+1) = 81?

• 2/3

• 1

• 1/3

• 1/2

In the alternative method for Example B, 64 is rewritten as a power of which number?

• 4

• 5

• 3

• 2

What is the value of x in the equation 2^(6x) = 2^4 using the alternative method?

• 1/2

• 1

• 2/3

• 3/4

What is the simplified form of 4/6?

• 1/2

• 2/3

• 3/4

• 1