Simple math im not understanding

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The discussion revolves around solving the equation 220*10^-3=(6/4.9)(1-e^((-t*4.9)/(140*10^-3)). The original poster seeks clarification on the steps leading to the solution of t=5.658, expressing confusion over their own calculation resulting in t=0.00566. Key operations discussed include dividing both sides by 6/4.9 and taking the natural logarithm of both sides. Participants emphasize the importance of correctly applying logarithmic properties and the exponential function in the calculations. The conversation highlights the need for a clearer understanding of the mathematical operations involved in solving the equation.
qwerty11
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Heres the solution I have:

220*10^-3=(6/4.9)(1-e^((-t*4.9)/(140*10^-3))
e^(-4.9t/(140*10^-3))=08203
t=5.658

Could somebody expand this more for me please so I can see the mathematical operations to get to this solution?
 
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qwerty11 said:
Heres the solution I have:

220*10^-3=(6/4.9)(1-e^((-t*4.9)/(140*10^-3))

Divide both sides by 6/4.9

qwerty11 said:
e^(-4.9t/(140*10^-3))=0.8203

take ln of both sides of the equation
 
rock.freak667 said:
Divide both sides by 6/4.9



take ln of both sides of the equation

When I divide 220*10^-3 I don't get the same answer.
 
I got t=0.00566
 
Shouldn't it be 220*10^-3/(6/4.9)=x
lnx=lne^...
lne^/lnx
=ans??
 
What is ln(ey)?
 

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