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Solve this log equation for x

Solve this log equation for x

Calculus 1 and 2 questions with single variable are posted here.

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Solve this log equation for x

Postby Kaka » Wed 08 June, 2011 16:16

`log (x-4) - log (3x - 10) = log (1/x)`
Kaka
 
Posts: 8
Joined: Sat 19 March, 2011 18:36

Re: Solve this log equation for x

Postby ChangBroot » Wed 08 June, 2011 16:23

If log of one thing is EQUAL to the log of "other thing," then the logs cancel out, and you're left with "one thing = other thing."


`log((x - 4)/(3x - 10)) = log(1/x)`
`(x - 4)/(3x - 10) = 1/x` Cross multiply

`x(x - 4) = 3x - 10` expand the left side

`x^2 - 4x = 3x - 10`

`x^2 - 7x + 10 = 0` factor out

`(x - 5)(x - 2) = 0` Therefore,

x = 5 and x = 2.

Hope this helps.
ChangBroot
 
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Joined: Fri 18 March, 2011 10:29


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