How do you solve ${ln x}^{2} = 2$ $Ln x^2 = 2$ ?

Question

2072 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-02T15:12:40

The solution is $x = e$ $x=e$ .

First you apply the rule of the log for the powers

$ln (x^{k}) = k ln (x)$ $ln(x^k)=kln(x)$ then, for you it is

$ln (x^{2}) = 2$ $ln(x^2)=2$

$2 ln (x) = 2$ $2ln(x)=2$

$ln (x) = 1$ $ln(x)=1$ .

Then, to obtain $x$ $x$ you need to apply the inverse operation of $ln$ $ln$ that is the exponential

$e^{ln (x)} = e^{1}$ $e^ln(x)=e^1$

$x = e$ $x=e$ .

How do you solve Ln x^2 = 2lnx2=2Ln x^2 = 2?