# Math Help - Equation problem (high school level math)

1. ## Equation problem (high school level math)

Hey guys Math newbie here.

I've been given an assignment, where I am to solve the equation, eg find t:

I've divided by 2,70 on both sides, but after that I'm completely lost. If someone could post a step-by-step solution, I'd be very happy!
Thank you all

/Cheers!

2. ## Re: Equation problem (high school level math)

We don't normally post solutions, but will help you to get the solution. You have divided through by 2,70, and so you have:

$\frac{1,5}{2,70}=1-e^{-0,021t}$

I would simplify the left by observing:

$\frac{1,5}{2,70}=\frac{15}{27}=\frac{5}{9}$ and so we have:

$\frac{5}{9}=1-e^{-0,021t}$

What do you think is a good next step towards isolating the variable $t$?

3. ## Re: Equation problem (high school level math)

Hey mate,
Thank you for your respons. I've tried a bit, but I'm still completely lost. I'm sure I'm doing something wrong.
I would use the rule:

To get:

And then use log to find t, but I know that's wrong :/

4. ## Re: Equation problem (high school level math)

The next thing you want to do is isolate the exponential term on one side, and everything else on the other.

Try adding $e^{-0,021}-\frac{5}{9}$ to both sides.

5. ## Re: Equation problem (high school level math)

Hey mate!
Thanks so much for your help!! I think I got it:

Right? :P

6. ## Re: Equation problem (high school level math)

I would finish it as:

$e^{-0,021t}=\frac{4}{9}$

$e^{0,021t}=\frac{9}{4}$

$0,021t=\ln\left(\frac{9}{4} \right)=2\ln\left(\frac{3}{2} \right)$

$t=\frac{2000\ln\left(\frac{3}{2} \right)}{21}\approx38.6157245817$

7. ## Re: Equation problem (high school level math)

Ah, thank you Yours is closer to the answer giving in my book (actually, the same), so I'll use that from now on!
Thank you for helping!