Question

find x if (2^5x) \2^x = 5√2^20

Answer 1

DEAR STUDENT,

Kindly refer to the attached paper for a detailed explanation and step by step elaborations with timely conditional insertions to get the final value or the required answer that is,

$\boxed{\bf{\underline{\therefore \quad x = 1}}}$

Hope my answer helps you and clears the doubts for finding the variable "x" !!!!!

Answer 2

Answer:

Required value of x is 1.

Step-by-step explanation:

By power of indices,we can solve this.

Given,

$\frac{ {2}^{5x} }{ {2}^{x} } = {( \sqrt[5]{2}) }^{20 }$

${2}^{5x - x} = { {2}^{20} }^{ \frac{1}{5} } \\ {2}^{4x} = {2}^{20 \times \frac{1}{5} } \\ {2}^{4x} = {2}^{20 \times \frac{1}{5} } \\ {2}^{4x} = {2}^{4} \\ 4x = 4 \\ x = \frac{4}{4} \\ x = 1$

The value of x is 1.

Here applied formulas are

${x}^{y} \times {x}^{d} = {x}^{y + d}$

${x}^{ {a}^{d} } = {x}^{ad}$

$\sqrt[x]{y} = {y}^{ \frac{1}{x} }$

$if \: \: {x}^{y} = {x}^{d} \: \: then \: \: y = d$