If $2^{2^{p}} = 256^{2^{4 p}}$ , then the value of p is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

-1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

-2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C -1
Given,

$2^{2^{p}} = 256^{2^{4 p}}$

$2^{2^{p}} = {(2^{8})}^{2^{4 p}}$

$2^{2^{p}} = 2^{8 \cdot 2^{4 p}}$

$\Rightarrow 2^{p} = 8 \cdot 2^{4 p}$

$2^{p} = 2^{3 + 4 p}$

$p = 3 + 4 p$

$∴ p = - 1$

Suggest Corrections

Similar questions

If $(3 x + \frac{1}{2}) (3 x - \frac{1}{2}) = 9 x^{2}$ -p then the value of p is
(a) 0 (b) $- \frac{1}{4}$ (c) $\frac{1}{4}$ (d) $\frac{1}{2}$

L : 1 s^{2} 2 s^{2} 2 p^{4}

Q : 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5}

P : 1 s^{2} 2 s^{2} 2 p^{6}, 3 s^{1}

R : 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}

2^{p + 2} + 2^{p + 1} = 96

p

p + \frac{1}{p} = 3

\frac{p^{4} + \frac{1}{p^{2}}}{p^{2} + 3 p + 1}

P (x) = x^{2}

P (a + 1) - P (a - 1)

Join BYJU'S Learning Program