Solve for unknown 6e^-3t = 3

[hbelle]

Here's my problem and I think I'm close but welcome any comments/corrections.
Solve for the unknown variable.
6e^-3t = 3
--------------------------------------
6e^-3t = 3
e^-3t = 3/6
ln e^-3t = ln 3/6
-3t = ln 3/6
t = ln 3/6 /-3

[Martingale]

Here's my problem and I think I'm close but welcome any comments/corrections.
Solve for the unknown variable.
6e^-3t = 3
--------------------------------------
6e^-3t = 3
e^-3t = 3/6
ln e^-3t = ln 3/6
-3t = ln 3/6
t = ln 3/6 /-3

if your answer is



then you are good

[hbelle]

Please help me understand
why the ln(3/6) changed to ln2 and
what happened to the negative -3, why did it change to positive?
thanks!

[hbelle]

Oh, log rule ln(x/y) = ln(x) - ln(y)
So:
-ln(3/6) becomes -ln(1/2)
= -(ln(1) - ln(2)) = - (0 - ln(2)) = ln(2)