Question

find x if (2^x x4^x)=(8)^1/3x32^1/5​

Answer 1

Answer:

x = 2/3

Step-by-step explanation:

Given an equation such that,

${2}^{x} \times {4}^{x} = {8}^{ \frac{1}{3} } \times {32}^{ \frac{1}{5} }$

To find the value of x.

We know that,

• ${a}^{m} \times {b}^{m} = {(ab)}^{m}$

Therefore, we will get,

$= > {(2 \times 4)}^{x} = {8}^{ \frac{1}{3} } \times {32}^{ \frac{1}{5} }$

But, we know that,

• $8 = {2}^{3}$
• $32 = {2}^{5}$

Substituting the values, we get,

$= > {8}^{x} = {2}^{3 \times \frac{1}{3} } \times {2}^{5 \times \frac{1}{5} } \\ \\ = > {8}^{x} = 2 \times 2 \\ \\ = > {( {2}^{3} )}^{x} = {2}^{2} \\ \\ = > {2}^{3x} = {2}^{2}$

Now, bases are same on both sides.

Therefore, power will also be same.

Therefore, we will get,

$= > 3x = 2 \\ \\ = > x = \frac{2}{3}$

Hence, the required value of x = 2/3.