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
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
-
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
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