Posted by mz deedee on Friday, November 11, 2011 at 12:00pm.
solve the logarithmic equation . express solution in exact form
log5(x9)+log5(x+4)=1+log5(x5)

precalculus  Steve, Friday, November 11, 2011 at 12:30pm
1 = log5(5), so we have
log5(x9)+log5(x+4)=log5(5)+log5(x5)
log5[(x9)(x+4)] = log5[5(x5)]
raise 5 to the powers, and we have
(x9)(x+4) = 5(x5)
x^2  5x  36 = 5x  25
x^2  10x  11 = 0
(x11)(x+1) = 0
Solutions are 11,1
However, 1 does not fit the original equation: log of negatives are undefined.

precalculus  Reiny, Friday, November 11, 2011 at 12:40pm
log5(x9)+log5(x+4)=1+log5(x5)
log5(x9)+log5(x+4)=log5(5)+log5(x5)
log5[(x9)(x+4)] = log5[5(x5)}
(x9)(x+4) = 5(x5)
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

Steve had right equation, precalculus  Reiny, Friday, November 11, 2011 at 12:43pm
I have an error in my equation...
x^2  10x  9 = 0 should be
x^2  10x  11  0 , just like Steve had
then (x11)(x+1) = 0
x = 11 or x = 1
so x = 11
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