Question

Helpppp plzzz !!! 13 points

Answer 1

Answer:

x = $\frac{-5}{2}$

Step-by-step explanation:

Given: $3^{4x - 5} = (\frac{1}{27})^{2x + 10}$

Since, xᵃ . xᵇ = xᵃ ⁺ ᵇ  we have

$3^{4x} . 3^{-5}$  = $\frac{1}{27^{2x + 10}}$

Since, 3³ = 27, we have: $3^{4x} . 3^{-5} = \frac{1}{3^{(3)(2x + 10)}}$

⇒ $3^{4x} . 3^{-5} = \frac{1}{3^{6x.30}}$

Also, $a^x. a^{-y} = \frac{a^x}{a^{y}}$

⇒ $\frac{3^{4x}}{3^5} = \frac{1}{3^{6x}.3^{30}}$

Cross-multiplying we get:

$3^{6x}.3^{30}.3^{4x} = 3^{5}$

⇒ $3^{10x} = \frac{3^{5}}{3^{30}} = 3^{-25}$

⇒$3^{10x} = 3^{-25}$

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

⇒ 10x = -25

⇒ x = $\frac{-5}{2}$.