Higher Maths- SOLVE: log (base:2) (X²-X + 10) - log (base:2) (5-X)
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Higher Maths- SOLVE: log (base:2) (X²-X + 10) - log (base:2) (5-X)

[From: ] [author: ] [Date: 12-01-07] [Hit: ]
......
log(base 2)(x^2 - x + 10) - log(base 2)(5 - x) = 3
log(base 2)((x^2 - x + 10)/(5 - x)) = 3
2^3 = (x^2 - x + 10)/(5 - x)
8 = (x^2 - x + 10)/(5 - x)
40 - 8x = x^2 - x + 10
0 = x^2 + 7x - 30
0 = (x + 10)(x - 3)
x = -10 or x = 3

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there's nothing to solve here, there's no equation

however, this expression can be simplified:

log_2 (x^2 - x + 10) - log_2 (5 - x) = log_2 [(x^2 - x + 10) / (5 - x)]

that's about it...the numerator and denominator have no common factors;

about the only other thing you could do would be to rewrite it using the change of base rule:

log_2 u (where u is the whole thing in brackets above) = ln u / ln 2
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