Maddy1251
  • Maddy1251
How do you solve the function ;; 10=1.5e^x and 6e^2x=7e^4x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Vocaloid
  • Vocaloid
for the first one, divide both sides by and take the natural log of both sides
Vocaloid
  • Vocaloid
*divide both sides by 1.5
Maddy1251
  • Maddy1251
@Vocaloid okay I was doing that, and got to In 6.66 = e^x

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Vocaloid
  • Vocaloid
good, now take the natural log ln(6.66) = x
Maddy1251
  • Maddy1251
x = about 1.9
Vocaloid
  • Vocaloid
good
Maddy1251
  • Maddy1251
For \[6e^{2x}=7e^{4x}\] How do you start that? I am getting these, I just iddn't know what you did with variables on each side
Vocaloid
  • Vocaloid
taking the natural log cancels out the e
Vocaloid
  • Vocaloid
ln(e^x) = x
Maddy1251
  • Maddy1251
Oh.. so it would be In(6)=In(7) basically, to get rid of the 'e' then bring down the exponents to be leading coeffications in front of the natural logs?
Vocaloid
  • Vocaloid
not quite
Vocaloid
  • Vocaloid
first we can divide both sides by 6, like so:|dw:1447186433166:dw|
Vocaloid
  • Vocaloid
then we can rewrite e^4x as (e^2x)*(e^2x) via the exponent rule
Vocaloid
  • Vocaloid
|dw:1447186523644:dw|
Maddy1251
  • Maddy1251
Would that cancel out the e^2x and leave one side with an e^2x or am I going the wrong way with that?
Vocaloid
  • Vocaloid
yeah, you're right
Vocaloid
  • Vocaloid
|dw:1447186586020:dw|
Maddy1251
  • Maddy1251
So 1 = 7/6(e^2x)?
Vocaloid
  • Vocaloid
yeah, then we divide both sides by (7/6)
Vocaloid
  • Vocaloid
|dw:1447186635640:dw|
Vocaloid
  • Vocaloid
then we take the natural log of both sides
Vocaloid
  • Vocaloid
|dw:1447186672243:dw|
Maddy1251
  • Maddy1251
x= (about) -0.077
Vocaloid
  • Vocaloid
great. is anything still unclear?
Maddy1251
  • Maddy1251
No. It makes sense now. The first one I had the answer, I doubted myself. The second one, I see now. I didn't know how to get it into a simplified form to solve. Thank you so much @Vocaloid !!

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