SOLUTION: Hi. This is for an AP Calculus Summer Assignment Please help {{{ 50e^(-x)= 30 }}} I don't even know where to start because I don't know how to handle the negative exponen

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi. This is for an AP Calculus Summer Assignment Please help {{{ 50e^(-x)= 30 }}} I don't even know where to start because I don't know how to handle the negative exponen      Log On


   

Question 766211: Hi. This is for an AP Calculus Summer Assignment

Please help
+50e%5E%28-x%29=+30+
I don't even know where to start because I don't know how to handle the negative exponent
Thank you
Found 3 solutions by solver91311, kmadison, rothauserc:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




But that doesn't really come into play in this problem.

Multiply both sides by



Take the natural log of both sides



Then use



and



To write



Then use



to write



Then multiply by -1



Your instructor might also be looking for



or



Any of the three forms is correct.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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Answer by kmadison(20) About Me  (Show Source):
You can put this solution on YOUR website!
First divide both sides by 50: e%5E%28-x%29+=+30%2F50+=+3%2F5+=+0.6
Now take the natural log of both sides: -x+=+ln%283%2F5%29
Finally, divide by -1 to get your final answer: x+=+-ln%283%2F5%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
50e^-x= 30
50 / e^x = 30 here apply exponent rule 4^-3 = 1/4^3
multiply both sides of = by e^x
30*e^x = 50
e^x = 50/30 = 5/3
log(e)5/3 = x this is log base e of 5/3 = x
ln 5/3 = x ln is the natural log
x = .51