Question

Can somebody please give a detailed solution for this sum

Answer 1

Answer:

c) 1407

Step-by-step explanation:

Let, λ = α .... (i)

$\alpha = log_{ {x}^{2} }( \sqrt{x \sqrt{x \sqrt{x} } } )$

$= > {x}^{2 \alpha } = \sqrt{x \sqrt{x \sqrt{x} } }$

$= > {x}^{2 \alpha } = \sqrt{x \sqrt{ {x}^{ \frac{3}{2} } } }$

$= > {x}^{2 \alpha } = \sqrt{x .{x}^{ \frac{3}{4} } }$

$= > {x}^{2 \alpha } = {x}^{ \frac{7}{8} }$

$= > 2 \alpha = \frac{7}{8}$

$= > \alpha = \frac{7}{16}$

so, λ = 7/16

Now,

$3216 \alpha = 3216 \times \frac{7}{16}$

$= 201 \times 7 = 1407$