Math 115 Carter Sample Test 2 Spring 2004
1. (2.5 points each) Compute the following (Hint: using a calculator will slow you down):
(a) log7(343)
(b) log1/2(1
512)
(c) log5(625)
(d) log4(2)
2. (2.5 points each) Use the rules of logarithms and exponentials to simplify the expres-
sions.
(a) 2 log6(x)+log
6(x−1) −3 log6(x+4)
(b) 122x+212−4−2x
(c) 3334log3334 (x+5)
(d) log56757 (5675742)
3. (2.5 points each) Given that logA(2) = 0.4307 logA(3) = 0.6826, logA(7) = 1.2091,
and logA(13) = 1.5937, compute
(a) logA(52)
(b) logA(2/9)
(c) logA(364)
(d) logA(49)
4. (10 points each) Sketch the graph of f(x).
(a) f(x)= x
x2−625
(b) f(x)=x−1
x−4
(c) f(x)=(x−4)(x+ 2)(x+1)
2
(d) f(x)=12
2x−5
(e) f(x)=4ln(x+1)
5. (5 points) Compute the difference quotient f(3+h)−f(3)
hfor the function f(x)=2
x.
1
