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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: 2,009 Thanks: 1042 
divide both sides by $0.04$ $\dfrac{1}{0.04} = \dfrac{1}{\frac{4}{100}}=\dfrac{100}{4}=25$ 
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: 1,050 Thanks: 430 
$\ 0.04t = ln \left ( \dfrac{2}{3} \right ) \implies \dfrac{\ 0.04t}{\ 0.04} = \dfrac{1}{\ 0.04} * ln \left ( \dfrac{2}{3} \right ) \implies$ $t = \ 25 * ln \left ( {2}{3} \right ) = 25 * ln \left \{ \left ( \dfrac{2}{3} \right )^{1} \right \} \implies$ $t = 25 * ln \left ( \dfrac{3}{2} \right ) = ln \left \{ \left ( \dfrac{3}{2} \right )^{25} \right \}.$ 
April 7th, 2018, 03:00 PM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,240 Thanks: 885  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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