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 April 5th, 2018, 11:22 PM #1 Newbie   Joined: Apr 2018 From: Israel Posts: 5 Thanks: 0 Exponential equation I don't understand how to pass from -0.04t = ln (2/3) to t= -25 X ln (2/3) Thank you in advance
 April 6th, 2018, 12:27 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402 divide both sides by $-0.04$ $-\dfrac{1}{0.04} = -\dfrac{1}{\frac{4}{100}}=-\dfrac{100}{4}=-25$ Thanks from Myriam
 April 6th, 2018, 01:20 AM #3 Newbie   Joined: Apr 2018 From: Israel Posts: 5 Thanks: 0 Thanks, But we divide only one side.
 April 6th, 2018, 12:47 PM #4 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 $-\ 0.04t = ln \left ( \dfrac{2}{3} \right ) \implies \dfrac{-\ 0.04t}{-\ 0.04} = \dfrac{1}{-\ 0.04} * ln \left ( \dfrac{2}{3} \right ) \implies$ $t = -\ 25 * ln \left ( {2}{3} \right ) = 25 * ln \left \{ \left ( \dfrac{2}{3} \right )^{-1} \right \} \implies$ $t = 25 * ln \left ( \dfrac{3}{2} \right ) = ln \left \{ \left ( \dfrac{3}{2} \right )^{25} \right \}.$ Thanks from topsquark and Myriam
April 7th, 2018, 03:00 PM   #5
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Quote:
 Originally Posted by Myriam Thanks, But we divide only one side.
No, we don't!!

We started with $\displaystyle -0.04t= ln(2/3)$. Dividing both sides by -0.04, we have $\displaystyle \frac{-0.04t}{-0.04}= \frac{1}{-0.04}ln(2/3)$.

On the left, the "-0.04" terms cancel (which was the reason we divided by -0.04 in the first place) to give just "t". On the right, as Romsek showed, $\displaystyle -\frac{1}{-0.04}ln(2/3)= -25 ln(2/3)$.

So the result of dividing on both sides by -0.04 is $\displaystyle t= -25 ln(2/3)$.

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