Why is it that -log(x+8)=4-log(x-7) has no solution? (they are log base 2)
2 answers:
Note that -log(x+8) + log(x-7) = 4, and that the left side is equal to
x-7
log -------------
x-8
Therefore,
x-7
log ------------- = 4
x-8
Acknowledging that your "log" actually represents "log to the base 2 of ... "
We get:
x-7
--------- = 2^4 = 16
x-8
Can this be solved for x?
Rearranging, x-7 = 16x - 128, or -7 = 15x - 128, or 121 = 15x
121
Dividing 121 by 15, we get x = ------- = 121/15 = approx. 8.067.
15
So far I see no reason why the given <span>-log(x+8)=4-log(x-7) "has no solution."</span>
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