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calculate the solution of the equation log(x+3)=3-log(x-3)
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We'll impose the constraints of existence of logarithms:
The interval of admissible solutions for the given equation is: (3 ; +infinite).
Now, we'll sove the equation, adding log(x-3) both sides:
log(x+3) + log(x-3) = 3
We'll apply the product rule:
log (x+3)(x-3) = 3
We'll recognize the difference of squares:
log (x^2 - 9) = 3
We'll take antilogarithm:
x^2 - 9 = 10^3
x^2 - 9 = 1000
We'll add 9 both sides:
x^2 = 1009
x1 = sqrt 1009
x1 = 31.764
x2 = -31.764
Since the 2nd value of the root doesn't belong to the range of admissible values, we'll reject it.
The only valid solution of the equation is:x = 31.764 (approx.)
Posted by giorgiana1976 on April 15, 2011 at 2:40 AM (Answer #1)
We need to find the solution for log(x+3)=3-log(x-3)
=> log(x+3) - log(x-3) = 3
use log a + log b = log (a*b)
=> log (x + 3)*(x - 3) = 3
=> (x + 3)*(x - 3) = 10^3
=> x^2 - 9 = 1000
=> x^2 = 1009
=> x = sqrt 1009 only as the log of a negative number is not defined.
The solution of the equation is x = sqrt 1009
Posted by justaguide on April 15, 2011 at 2:43 AM (Answer #2)
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