Question

Determine the value of x? ​

Answer 1

x=6, -1

Explanation:

Using the rule of exponents:

a^{m} ÷ a^{n} = a^{(m-n)} , then

aˣ² ÷ a^{5x} = a⁶

⇒ a^{x^2 - 5x} = a⁶

⇒ x² - 5x = 6

x² - 5x - 6 = 0

(x - 6)(x + 1) = 0 [middle term splitting]

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6 ║ x + 1 = 0 ⇒ x = -1

Answer 2

see explanation

Explanation:

Using the rule of exponents

`a^(m)` ÷
`a^(n)` =
`a^((m-n))`, then

`a^(x^2-5x)` =
`a^(6)`, hence

x² - 5x = 6 ( subtract 6 from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 1