Math Help - Help simplifying expression

1. Help simplifying expression

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

The answer is t=ln2/.003

2. Re: Help simplifying expression

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

The answer is t=ln2/.003
use $ln(e^x)=x \cdot ln(e)=x$

3. Re: Help simplifying expression

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, $y= e^{.003t}$. 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".

So we would start with
$y= e^{.003t}$ and first take the logarithm of both sides: $ln(y)= .003t$.
Now, divide both sides by .003: $\frac{ln(y)}{.003}= t$.