Alexander B. answered • 09/13/15
Tutor
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(7)
PhD in Engineering with 20 yrs of Math and Science Teaching Experience
Hello Diane,
The solution is following:
In x + In (x+2) =2
ln(x*(x+2))=2
x2 + 2x - e2 = 0
or approximately:
x2 + 2x - 7.389056 = 0
This canonical quadratic equation can be solved either manually (long way), or using online Quadratic Equation Solver at : http://examn8.com/QuadraticEquations.aspx (sort of shortcut)
There are 2 solutions for x:
x1= 1.89638
x2= -3.89638
x2= -3.89638
but the second one should be discarded (no logarithm of the negatives). Thus the only correct answer (rounded) is 1.89638. Note: this value corresponds to the exact solution √(1+e2)-1.
Hope this may help.
Alexander B.
I know that; the answer provides the exact solution and a rounded decimal value as it's clearly stated. Two rounded values are shown in order to exclude the non-conforming one (negative). Best regards,
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09/13/15
Mark M.
Not what you wrote:
Thus the only correct answer (rounded) is 1.89638. Note: this value corresponds to the exact solution √(1+e2)-1.
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09/13/15
Alexander B.
That's right: there is an exact solution √(1+e2)-1 shown and also a rounded decimal value 1.89638, which corresponds to that exact solution w/some rounding error as it's clearly stated. This estimate is included just for added clarity: for any experienced math student it's relatively easy to see that the value of the expression is positive, thus it should be valid (unlike that second one -1-√(1 + e2) included in your original solution). Best regards,
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09/14/15
Mark M.
09/13/15