Question

Plzzzz solve is briefly

Answer 1

I hope it may help you

Answer 2

Answer:

$\implies \: \red{\boxed{ x = \frac{7}{16} }}$

Step-by-step explanation:

Solution

According to the question,

$\implies \: {2}^{x} = {4}^{y} = {8}^{z}$

We can write it,

$\implies \: {2}^{x} = {2}^{2y} = {2}^{3z}$

Now comparing on each sides ,

We get,

$x \: = 2y = 3z \\ \\ \implies \: z \: = \frac{x}{3} \\ \\ \implies \: y = \frac{x}{2}$

Now , substitute these values ,

$\implies \: \frac{1}{2x} + \frac{1}{4y} + \frac{1}{4z} = 4 \\ \\ \implies \: \frac{1}{2x} + \frac{1}{4 \times \frac{x}{2} } + \frac{1}{4 \times \frac{x}{3} } = 4 \\ \\ \implies \: \frac{1}{2x} + \frac{1}{2x} + \frac{3}{4x} = 4 \\ \\ \implies \: \frac{2 + 2 + 3}{4x} = 4 \\ \\ \implies \: 7 = 16 \: x \\ \\ \implies \: \boxed{ x = \frac{7}{16} }$