# Help simplifying expression

• Jul 31st 2011, 10:44 PM
benny92000
Help simplifying expression
How do you solve this expression for T? 2=e^(.003t)

• Jul 31st 2011, 11:49 PM
abhishekkgp
Re: Help simplifying expression
Quote:

Originally Posted by benny92000
How do you solve this expression for T? 2=e^(.003t)

use $\displaystyle ln(e^x)=x \cdot ln(e)=x$
In general, to "solve" an equation for t, you do, to both sides, the "opposite" of what is done to t, in the reverse order. Here, $\displaystyle y= e^{.003t}$. To evaluate that, you would do two things: first multiply t by 0.003, then take the exponential. We need to do the "opposite" (inverse) of the exponential, then the "opposite" of "multiply by 0.003". The inverse of the exponential function is the natural logarithm and the inverse of "multiply by 0.003" is "divide by 0.003".
$\displaystyle y= e^{.003t}$ and first take the logarithm of both sides: $\displaystyle ln(y)= .003t$.
Now, divide both sides by .003: $\displaystyle \frac{ln(y)}{.003}= t$.