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x=?Calculate x if log2x=log5+log(x-24/5)
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We'll establish the constraints of existence of logarithms:
x - 24/5>0
x > 24/5
The range of admissible values for x is (24/5 ,+inf.).
We'll apply quotient property of logarithms:
log 2x = log 5 - log (x - 24/5)
log 2x = log [5/(x - 24/5)]
Since the bases of logarithms are matching, we'll apply the one to one property:
2x = 5/(x - 24/5)
We'll cross multiply;
2x(x - 24/5) = 5
We'll remove the brackets:
2x^2 - 48x/5 - 5 = 0
We'll multiply by 5:
10x^2 - 48x - 25 = 0
We'll apply the quadratic formula:
x1 = [48+sqrt(2304+1000)]/40
x1 = 2(24+sqrt826)/40 = 2.637 < 24/5
x2 = 2(24-sqrt826)/40 = -0.2< 24/5
Since the values of x1 and x2 are not in the interval of admissible values, the equation has no solutions.
Posted by giorgiana1976 on May 11, 2011 at 6:02 AM (Answer #2)
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