Math 111 – Chapter 5 Sample Test
Show all work. Simplify all answers. Leave all answers exact (reduced fractions not rounded decimals
– unless otherwise indicated). Note that some answers will include logarithms that cannot be simplified.
1) Find the inverse of f (x) =
3
x!5
2) Find the inverse of f (x) = 5x 3 ! 2
! 1$
3) Graph f (x) = # &
" 2%
x
4) Graph f (x) = !3x
5) Graph f (x) = e x ! 1 . Note: e ! 2.72, e2 ! 7.39, e"1 ! 0.37
The remainder of the problems on this test are worth 5 points apiece.
6) Simplify log 5 125
7) Simplify ln(1)
1
8) Simplify log10 4
9) Convert to a logarithmic equation: 4 !3 =
1
64
10) Convert to an exponential equation: log x 3 = !2
11) Express in terms of sums and differences of logarithms. ln
2
3x 3
12) Express in terms of sums and differences of logarithms. log wr 3
13) Express as a single logarithm and simplify if possible. log14 2 + log14 7
14) Express as a single logarithm and simplify if possible. 3log x ! 4 log y + 12 log z
15) Simplify 3log 3 4 x
16) Simplify log b b 3
17) Solve 4 2 x!1 ! 3 = 61
18) Solve 31! x = 9 2 x
19) Solve e! x ! 5 = 10
20) Solve log 3 (10 + 5x) = 2
21) Solve log 2 x + log 2 (x ! 2) = 3
22) Solve ln(x + 8) + ln(x ! 1) = 2 ln x
23) A population is growing exponentially at a rate of 3% per year.
a) How long will it take to double?
b) If you start with a population of 10, what will the population be in 5 years?
24) You deposit $100 into a continuously compounding bank account. Five years later the account
contains $150. What is the interest rate of the account?