log11 (2x-9) + log11 x=1?

Answer 1

Since log a + log b = log ab, the equation becomes
log [base 11] x(2x - 9) = 1
Hence
x(2x-9) = 11
that is
2x^2 - 9x - 11 = 0
(2x-11)(x+1) = 0
therefore
2x - 11 = 0 or x+1 = 0
The second gives x = -1 which is not allowable, as the log of a negative number is not a "real" number. hence the only solution is
2x = 11
x = 5.5

PS I see someone beat me to the answer, but you notice that the second solution must be excluded.

Answer 2

Addition of logs is really multiplication so the problem becomes:
log11 x (2x-9)=1
log11 x (2x-9)= log11 11
2x^2-9x=11
2x^2-9x-11=0
(2x-11)(x+1)=0
x= -1 or x= 11/2
x= -1 does not work (logs of negative numbers do not exist)

Answer 3

log11 (2x - 9) + log11 x = 1
log 11 (2x^2 - 9x) = log11 11
2x^2 - 9x - 11 = 0
(2x - 11)(x + 1) = 0
x = 5.5 or x = -1

x = -1 rejected for logarithms to be defined.
Therefore, the only solution is x = 5.5

Answer 4

sums of logs are products. antilog of 1 = base of log so you have the product of two terms = 11 once you take antilog11 of both sides.

the disbelief is left to the student...