Question

How would you solve this?

Answer 1

The equation has three solutions:

x=
`(1)/(2) + (1)/(2) log_(2) (3)`

x=1

x =
`(1)/(2)`

Explanation:

||
`4^(x) - 3`|
`-2`| = 1

|
`4^(x) - 3`|
`-2` = 1 |
`4^(x) - 3`|
`-2` = - 1

|
`4^(x) - 3`| = 1+2 |
`4^(x) - 3`| = -1+2

|
`4^(x) - 3`|=3 |
`4^(x) - 3`| = 1

`4^(x) - 3` =3
`4^(x) - 3` = - 3
`4^(x) - 3` = 1
`4^(x) - 3` = - 1

x=
`(1)/(2) + (1)/(2) log_(2) (3)` x∉∅ x=1
`x = (1)/(2)`

The union of these four solutions is:
`(1)/(2) , 1,`
`(1)/(2) + (1)/(2) log_(2) (3)`

I hope this is clearly and understandably written to you :)

Answer 2

It would have 3 solutions
if you solve the equation how it is, it give 1 solution but if you make the 1 negative you get 2 more possibilities