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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 $\displaystyle t= -25 ln(2/3)$. Tags equation, exponential Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post MrNish Algebra 5 October 24th, 2013 08:47 AM panky Algebra 7 January 16th, 2012 05:34 PM dharani_sabba Elementary Math 2 March 22nd, 2011 01:09 AM Silkenos Algebra 1 December 5th, 2010 07:50 PM jiripo Algebra 21 October 21st, 2010 05:00 PM

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