Question

Helpppp plzzz !!! 13 points

Answer 1

x =
`$ (-5)/(2) $`

Explanation:

Given:
`$ 3^(4x - 5) = ((1)/(27))^(2x + 10) $`

Since, xᵃ . xᵇ = xᵃ ⁺ ᵇ we have

`$ 3^(4x) .  3^(-5) $` =
`$ (1)/(27^(2x + 10)) $`

Since, 3³ = 27, we have:
`$ 3^(4x) .  3^(-5) = (1)/(3^((3)(2x + 10))) $`

⇒
`$ 3^(4x) . 3^(-5) = (1)/(3^(6x.30)) $`

Also,
`$ a^x. a^(-y) = (a^x)/(a^(y)) $`

⇒
`$ (3^(4x))/(3^5)  = (1)/(3^(6x).3^(30)) $`

Cross-multiplying we get:

`$ 3^(6x).3^(30).3^(4x) = 3^(5) $`

⇒
`$ 3^(10x) = (3^(5))/(3^(30)) = 3^(-25) $`

⇒
`$ 3^(10x) = 3^(-25) $`

Since the bases are same, the powers should be equal.

⇒ 10x = -25

⇒ x =
`$ (-5)/(2) $`.