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Unformatted text preview: ] (c) ln10 - ln ( 7 - x ) = ln x We will work this equation in the same manner that we worked the previous one. We’ve got two
logarithms on one side so we’ll combine those, drop the logarithms and then solve. æ 10 ö
÷ = ln x
10 = x ( 7 - x )
10 = 7 x - x 2
x 2 - 7 x + 10 = 0 ( x - 5 )( x - 2 ) = 0 Þ x = 2, x = 5 We’ve got two possible solutions to check here. x = 2: ln10 - ln ( 7 - 2 ) = ln 2
ln10 - ln 5 = ln 2 This one is okay. x = 5: ln10 - ln ( 7 - 5 ) = ln 5
ln10 - ln 2 = ln 5 This one is also okay. In this case both possible solutions, x = 2 and x = 5 , end up actually being solutions. There is
no reason to expect to always have to throw one of the two out as a solution.
[Return to Problems] Now we need to take a look at the second kind of logarithmic equation that we’ll be solving here.
This equation will have all the terms but one be a logarithm and the one term that doesn’t have a
logarithm will be a constant.
In order to solve these kinds of equations we will...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12