1. 0.5^3x-2 = 14
0.5^3x = 14+2 = 16
Take Log of both sides:
3x*Log 0.5 = Log 16
Divide both sides by Log 0.5:
3x = Log 16/Log0.5 = -4
Divide both sides by 3:
X = -4/3
2. Log(x-1)-Log x = Log(x-3)
Log((x-1)/x) = Log(x-3)
B. f(x) = (x+2)/x; g(x) = 7/(x-5)
a. F(g(x)) = (7/(x-5)+2)/(7/(x-5)) =
((2x-3)/(x-5))*(x-5)/7 = (2x-3)/7.
b. Domain: All real values of X.
-Infinity < X < +Infinity.
c. g(F(x)) = 7/((x+2)/x-5)=
7/(x+2-5x)/x = 7/(x+2-5x)/x =
7/(2-4x)/x = 7x/(-2(2x-1))
d. 2x-1 = 0
2x = 1
X = 1/2 Will result in a denominator of zero and the Eq becomes undefined.
DOMAIN: All real values of X except 1/2.
X <> 1/2.
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