/sci/ - Science & Math

>>12253008
Remember what [math]x = \log_a b[/math] actually is. It is the number [math]x[/math] such that [math]a^x = b[/math]. Now, [math]e^{\ln(x^a)} = x^a = (e^x)^a=(e^{\ln(x)})^a = e^{a\ln(x)}[/math]. If you then use the fact that the exponential function is injective, you will get that [math]\ln(x^a) = a\ln(x)[/math]. You can replace the base number with any positive real (and the logarith correspondingly) and it will still be true.

>>12183626
What else is there to do, though?

>>12183708
Find something interesting, then find a suitable supervisor and ask them if they would be interested in working with you on a topic related to your interests. Then formulate the thing together, or just go with your idea if you already have a concrete vision of what you want to do and the supervisor agrees with your plan.