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 ln e ^x - ln e^2 = ln e^7

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samerrima | Student, Grade 9 | (Level 1) Honors

Posted July 13, 2010 at 5:46 AM via web

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 ln e ^x - ln e^2 = ln e^7

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted July 13, 2010 at 5:48 AM (Answer #1)

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ln e^x - ln e^2 = ln e^7

We know that ln e^x = xlne

Also we know that ln e = 1

Now let us substitute:

x ln e -2ln e = 7 ln e

x*1 -2*1 = 7*1

==> x-2 = 7

Add 2 to both sides:

==> x = 7+2 = 9

The answer is x=9

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kjcdb8er | Teacher | (Level 1) Associate Educator

Posted July 13, 2010 at 5:50 AM (Answer #2)

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the natural log of e^x is x. Thus:

ln(e^x) = x

ln(e^2) = 2

ln (e^7) = 7

So this equation becomes:

x - 2 = 7

x = 9

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neela | High School Teacher | (Level 3) Valedictorian

Posted July 13, 2010 at 8:37 AM (Answer #3)

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lne^x - lne^2=lne^7.

Solution:

By definition, ln e^a = a.

So lne^x =x, lne^2 =2 and  lne^7 =7. Therefore the given equation could now be rewritten as:

x -2=7 Or

x = 7+2 = 9.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted July 13, 2010 at 8:37 PM (Answer #4)

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First, let's recall the property that ln e  =1.

Now, we'll use the power property of logarithms, so that:

ln e^2 = 2ln e  =2

ln e^7 = 7ln e = 7

 ln e ^x = xln e = x

Now, we'll re-write the equation:

x - 2 = 7

We'll add 2 both sides:

x = 7+2

x = 9

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