SOLUTION: Solve the equation if possible. 12e^8t-e=8e^8t I don't really know how to go about solving this. Do I subtract the 12e^8t to the other side first, or something else? Also, it's

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Question 278941: Solve the equation if possible.
12e^8t-e=8e^8t
I don't really know how to go about solving this. Do I subtract the 12e^8t to the other side first, or something else? Also, it's possible that the answer doesn't exist or that the exact answer doesn't exist. Please help!
Found 3 solutions by Alan3354, Edwin McCravy, solver91311:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!

Subtract 8e^8t




8t-1 = ln(1/4)
8t = 1 + ln(1/4)
t = (1 + ln(1/4))/8
t =~-0.048286795
Answer by Edwin McCravy(20062)   (Show Source): You can put this solution on YOUR website!








Divide both sides by e



Notice that e is raised to the first power on the
left bottom, so you subtract exponents:





Take natural logs of both sides:



Use laws of logarithms:



Use another law of logarithms:







Divide both sides by 8

 or about -.0482867951

Edwin
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




Yes, the first step is to put both of the terms on one side. Just for the sake of what I consider to be neatness, I'm going to add to both sides, with the following result:



Next, take the natural log of both sides:



The log of the product is the sum of the logs, so:



The log of a base raised to a power is the power times the log of the base:



Since we know that



Add to both sides:



Multiply by



John
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