Posted by mz deedee on Friday, November 11, 2011 at 12:00pm.
1 = log5(5), so we have
log5(x-9)+log5(x+4)=log5(5)+log5(x-5)
log5[(x-9)(x+4)] = log5[5(x-5)]
raise 5 to the powers, and we have
(x-9)(x+4) = 5(x-5)
x^2 - 5x - 36 = 5x - 25
x^2 - 10x - 11 = 0
(x-11)(x+1) = 0
Solutions are 11,-1
However, -1 does not fit the original equation: log of negatives are undefined.
log5(x-9)+log5(x+4)=1+log5(x-5)
log5(x-9)+log5(x+4)=log5(5)+log5(x-5)
log5[(x-9)(x+4)] = log5[5(x-5)}
(x-9)(x+4) = 5(x-5)
x^2 - 5x - 36 = 5x - 25
x^2 - 10x - 9 = 0
x = (10 ± √136)/2 = appr. 10.83 or -.83
but for each of the above to defined, x > 9
so x = (10 + √136)/2 = 5 + √34
check my arithmetic
I have an error in my equation...
x^2 - 10x - 9 = 0 should be
x^2 - 10x - 11 - 0 , just like Steve had
then (x-11)(x+1) = 0
x = 11 or x = -1
so x = 11
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