Question

How do you solve `(log(x))^2=4`?

Answer 1

`x=10^2` or `x=10^-2`

Explanation:

`(Log(x))^2=4`
`implies (Log(x))^2-2^2=0`

Use formula named as Difference of Squares which states that if `a^2-b^2=0`, then `(a-b)(a+b)=0`

Here `a^2=(Log(x))^2` and `b^2=2^2`

`implies (log(x)-2)(log(x)+2)=0`

Now, use Zero Product Property which states that if the product of two number, say `a` and `b`, is zero then one of two must be zero, i.e., either `a=0` or `b=0`.

Here `a=log(x)-2` and `b=log(x)+2`

`implies` either `log(x)-2=0` or `log(x)+2=0`
`implies` either `log(x)=2` or `log(x)=-2`
`implies` either `x=10^2` or `x=10^-2`