The value of x is ±0.7071 and x is an irrational number
<h3>How to solve for x?</h3>
The equation is given as:
![4x^2 = 2](https://tex.z-dn.net/?f=4x%5E2%20%3D%202)
Divide by 4
![x^2 = 0.5](https://tex.z-dn.net/?f=x%5E2%20%3D%200.5)
Take the square roots
![x = \pm 0.7071](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%200.7071)
Hence, the value of x is ±0.7071
<h3>How to prove that x is irrational?</h3>
The equation is given as:
![4^x = 5](https://tex.z-dn.net/?f=4%5Ex%20%3D%205)
Take the logarithm of both sides
![x\log(4) = \log(5)](https://tex.z-dn.net/?f=x%5Clog%284%29%20%3D%20%5Clog%285%29)
Divide both sides by log(4)
x = 1.16096....
The above number is a non-terminating decimal.
Non-terminating decimals cannot be represented as fractions of two integers
Hence, x is an irrational number
Read more about irrational numbers at:
brainly.com/question/17450097
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