There's a very well known rule that says that
[math]log_a (b^n) = nlog_ab[/math]
But I've come across something that has me a bit confused. Consider this equation:
[math]ln(x)^2 = 1[/math]If you solve it using the classing method of exponentiating both sides of the equation, you get
[math]x^2 = e[/math]which has solutions for x equals to [imath]-\sqrt(e)[/imath] and [imath]\sqrt(e)[/imath]
But if you use the aforementioned rule and take the exponent out of the logarithm, you get
[math]2lnx = 1[/math][math]lnx = 1/2[/math][math]x = \sqrt(e)[/math]Which doesn't include part of the solution. What am I missing here?
[math]log_a (b^n) = nlog_ab[/math]
But I've come across something that has me a bit confused. Consider this equation:
[math]ln(x)^2 = 1[/math]If you solve it using the classing method of exponentiating both sides of the equation, you get
[math]x^2 = e[/math]which has solutions for x equals to [imath]-\sqrt(e)[/imath] and [imath]\sqrt(e)[/imath]
But if you use the aforementioned rule and take the exponent out of the logarithm, you get
[math]2lnx = 1[/math][math]lnx = 1/2[/math][math]x = \sqrt(e)[/math]Which doesn't include part of the solution. What am I missing here?