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April 5th, 2018, 11:22 PM   #1
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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
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April 6th, 2018, 12:27 AM   #2
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divide both sides by $-0.04$

$-\dfrac{1}{0.04} = -\dfrac{1}{\frac{4}{100}}=-\dfrac{100}{4}=-25$
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April 6th, 2018, 01:20 AM   #3
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Thanks,

But we divide only one side.
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April 6th, 2018, 12:47 PM   #4
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$-\ 0.04t = ln \left ( \dfrac{2}{3} \right ) \implies \dfrac{-\ 0.04t}{-\ 0.04} = \dfrac{1}{-\ 0.04} * ln \left ( \dfrac{2}{3} \right ) \implies$

$t = -\ 25 * ln \left ( {2}{3} \right ) = 25 * ln \left \{ \left ( \dfrac{2}{3} \right )^{-1} \right \} \implies$

$t = 25 * ln \left ( \dfrac{3}{2} \right ) = ln \left \{ \left ( \dfrac{3}{2} \right )^{25} \right \}.$
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April 7th, 2018, 03:00 PM   #5
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Quote:
Originally Posted by Myriam View Post
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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