## Solve for unknown 6e^-3t = 3

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
hbelle
Posts: 9
Joined: Fri May 28, 2010 1:52 am

### Solve for unknown 6e^-3t = 3

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
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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### Re: Solve for unknown 6e^-3t = 3

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

$t = \frac{\ln\left(\frac{3}{6}\right)}{-3}=\frac{\ln(2)}{3}$

then you are good

hbelle
Posts: 9
Joined: Fri May 28, 2010 1:52 am

### Re: Solve for unknown 6e^-3t = 3

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

hbelle
Posts: 9
Joined: Fri May 28, 2010 1:52 am

### Re: Solve for unknown 6e^-3t = 3

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)