$\log x^2 = 3, x > 0$
If I enter a negative number like this
$\log ((-2)^2) = 3, x > 0$
It is valid right?
When it just says $\log x^2$ what is applied first? Log or the exponential?
$\log x^2 = 3, x > 0$
If I enter a negative number like this
$\log ((-2)^2) = 3, x > 0$
It is valid right?
When it just says $\log x^2$ what is applied first? Log or the exponential?
It's sometimes all about the restrictions. To solve: $\log (x^2) = 3$, $x > 0$, we interpret this as "Solve $\log(x^2) = 3$, but only give answers $x$ that are greater than $0$".
First take both sides as exponents on 10:
$ \log (x^2) = 3 $ $10^{\log (x^2)} = 10^3 $ $x^2 = 1000, \textrm{by properties of $\log$}$ $x = \pm \sqrt{1000} \approx \pm 31.6227766$
So without restrictions, we would say $x = \pm 31.6227766$, however, with the restriction that $x > 0$, we must only choose the positive result:
$ x = 31.6227766. $