Can someone explain step by step how to make x the subject in an exponential equation?

I know the general form is y = ae^kx
So the just say I need to find out at what time would the experiment be at its half life which is 50, so I sub 50 into the following equation:

y = 92.776e^(-0.701t)
50=92.776e^(-0.701t)

I'm really bad at exponentials, could someone help? Step by step would be much appreciated :)

also another question,

lnY= mX + ln k

What is the step by step method to make Y the subject? :)
Thank you in advance...

DD

Ok, here it goes:



Put log on both sides:











However, I don't quite know what you want concerning the half life.

For the second one,





It's the reverse of the previous process; here's the rule:

[QUOTE]Can someone explain step by step how to make x the subject in an exponential equation?
/QUOTE]

Just remember that

That removes the exponent from the equation and makes it solvable by normal algebra. If it's in the form



you need to take the logarithm of both sides, first.