Question

Solve for X if
(X/2)^log2 X = 8X

(A) 1/4. (B) 1/2. (C) 1 (D) 2.

SOLVE FAST!!

Answer 1

Given:

Equation: $(\frac{x}{2})^{\text{log}_{2}(x)}=8x$

To Find:

Value of 'x'.

Solution:

$(\frac{x}{2})^{\text{log}_{2}(x)}=8x$

Let $\text{log}_2(x)=y$

x = $2^{y}$

Now rewrite the given equation as,

$(\frac{2^y}{2})^y=8(2^y)$

$(2^{y-1})^{y}=2^{3}(2^y)$

$2^{y(y-1)}=2^{y+3}$

By comparing exponents of both the sides of the equation,

y(y - 1) = y + 3

y² - y = y + 3

y² - 2y - 3 = 0

y² - 3y + y - 3 = 0

y(y - 3) + 1(y - 3) = 0

(y - 3)(y + 1) = 0

y - 3 = 0

y = 3

(y + 1) = 0

y = -1

For y = 3,

$x=2^3$

x = 8

For y = -1

x = $2^{-1}$

x = $\frac{1}{2}$

From the given options, x = $\frac{1}{2}$ will be the answer.

Option (B) will be the correct option.

Answer 2

Answer:

(B) ½

Step-by-step explanation:

see image for solution

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