Question

Solve 64^x = 16^(x−1). (1 point) Select one: a. x = −2 b. x = −1 c. x = negative 1 over 4 d. x = negative 1 over 3

Answer 1

`\huge \boxed{x=-2}`

Explanation:

64^x = 16^(x-1)

Rewrite the bases with base of 4.

(4^3)^x = (4^2)^(x-1)

Multiply exponents.

4^(3x) = 4^(2(x-1))

Cancel same bases.

3x = 2(x-1)

Expand brackets.

3x = 2x - 2

Subtract 2x from both sides.

x = -2

Answer 2

a. x = -2

Explanation:

64ˣ = 16⁽ˣ⁻¹)

64 = 4³

16 = 4²

4³⁽ˣ⁾ = 4²⁽ˣ⁻¹)

4³ˣ = 4²ˣ⁻²

3x = 2x - 2

x = -2