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Topic: Help with logarithms
Replies: 6   Last Post: Sep 20, 2006 12:21 AM

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Vijaya Prasad Nalluri

Posts: 8
From: India
Registered: 4/10/06
Re: Help with logarithms
Posted: Sep 18, 2006 5:58 PM
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> Can somebody help me solve this problems?
>
> 1) lnx + lnx^2 + lnx^3 + lnx^4 + lnx^5 = 5
>
> The answer is sqrt[3](e)
>
> 2) lnx - ln(2x+1) = ln1/x
>
> The answer is x=1 + sqrt(2)


1)The equation simplifies to
ln(x.x^2.x^3.x^4.x^5) = 5,
ln(x^(1+2+3+4+5)) = 5,
ln(x^15) = 5,
15 ln(x) = 5,
ln(x) = 1/3,
x = e^(1/3) = cuberoot of e.
2)ln(x /(2x+1)) = ln(1/x),
x /(2x+1) = 1 / x,
x^2 = 2x + 1,
x^2 - 2x = 1,
x^2 - 2x + 1 = 2,
(x - 1)^2 = 2,
x - 1 = + sqrt(2),(the other value of x - 1 is
- sqrt(2)which makes x negative)
So x = 1 + sqrt(2)



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