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-3+e^(x+1)=2+e^(x-2)Pliz help me to solve this questions...3 marks...but this question...
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High School Teacher
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Posted by embizze on April 30, 2012 at 10:59 AM (Answer #1)
You need to solve the equation using the laws of exponentials such that:
`-3+e^(x+1)=2+e^(x-2) =gt e^(x+1) - e^(x-2) = 2+3 `
`e^x*e - e^x*e^(-2) = 5 `
You need to factor out `e^x` such that:
`e^x(e - 1/e^2) = 5`
`e^x = 5/(e - 1/e^2)`
You need to take logarithms such that:
`ln e^x = ln(5/(e - 1/e^2))`
`x*ln e =ln(5/(e - 1/e^2))`
You need to remember that ln e = 1 such that:
`x =ln((5e^2)/(e^3 - 1))`
`x = ln 5e^2 - ln(e^3 - 1)`
`x = ln 5 + 2 ln e - ln(e^3 - 1)`
`x = ln 5 + 2 - ln(e^3 - 1)`
Since `e^3 gt 1` , hence `e^3 - 1 gt 0` , thus it is possible to evaluate `ln(e^3 - 1).`
Hence, evaluating the solution to the given equation yields x = `ln 5 + 2 - ln(e^3 - 1).`
Posted by sciencesolve on April 30, 2012 at 3:02 PM (Answer #3)
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