Math
posted by Jeff on .
Can you show me the work to get these answers also?
A.Solve each equation. Leave exact answers:
1.5^3x2=14
2.log(x1)logx=log(x3)
B.If f(x)=x+2/x and g(x)=7/x5,
a. Find the composition (f o g)(x) and simplify completely.
b. Find the domain of (f o g)(x).Write answer in interval notation.
c. Find the composition of (g o f)(x) and simplify completely.
d. Find the domain (g o f)(x).Write your answer using interval notation.

1. 0.5^3x2 = 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(x1)Log x = Log(x3)
Log((x1)/x) = Log(x3)
B. f(x) = (x+2)/x; g(x) = 7/(x5)
a. F(g(x)) = (7/(x5)+2)/(7/(x5)) =
(7+2(x5)/(x5))/(7/(x5)) =
((2x3)/(x5))/(7/(x5)) =
((2x3)/(x5))*(x5)/7 = (2x3)/7.
b. Domain: All real values of X.
Infinity < X < +Infinity.
c. g(F(x)) = 7/((x+2)/x5)=
7/(x+25x)/x = 7/(x+25x)/x =
7/(24x)/x = 7x/(2(2x1))
d. 2x1 = 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.