1.  log 100,000

2.  log₃27

3.  log₆1

4.  log₂\/2

5.  ln e⁷

6.  log₃3⁵

_{7.  log 10}x + ₁₀^log10^4x

8.     1      +      1
     log₇x        log₂x

9.  64 ^log16^x

10.  ln (1/e^z)

11.  (log₃5)(log 4)(log₂7)

12.  log x⁴ + 2 log (y/x) - log (y²/x)

13.  log₄3 + log₄5

14.  3 log x + (1/4) log y

15.  (1/2)(log₂x + log₂y - log₂z)

16.  ln 4 - ln 3 - 2 ln 5

17.  ln e³

18.  e^{3 ln x}

19.  10^{5 + log 2}

20.  (3^-1 - 5^-2)^-1

21.  (32^3/5)^1/3

22.  2x^3/4 + 4x^1/4
            2x^-1/4

23.  ( ³\/x² )( ⁶\/x⁵ )

24.  Graph and find the domain and range:

        a.  y = e^|x|                   b.  y = e^x-2               c.  y = e^x + 1

        d.  y = |e^x - 4|             e.  y = log x - 3        f.  y = 2 log x

        g.  y = log (3x)            h.  y = |log x| - 1

25.  If log₃4 = x and log₃6 = y, find

        a.  log₃24                    b.  log₃8                    c.  log₃4.5

26.  Solve for x:

        a.  log x = 4            b.  ln x = 3            c.  ln |x| = 4            d.  ln (ln x) = 2

        e.  (log x)² = 9        f.  log x = 0.3        g.  e^x = 8

        h.  log₃(x - 1) - log₃(x + 2) = 1            i.  log₂(x - 1) + log₂(x - 1)  = 2

        j.  4^x = 7                k.  (e^x)² = 100        l.  9^x = ³\/(27/9^x)

        m.  5^2x - 3(5^x) + 2 = 0                        n.  e^2x + e^x - 12 = 0

        o.  x⁴ = 32            p.  log₂x + log₂(x - 1) = 0

        q.  log₅(log₃x) = 1                                r.  ln (x - 1) + ln (2x - 1) = 2 ln x

        s.  2^x-1 = 5^2x+3     t.  e^x - 2e^-x = 8        u.  x³ = x^{log x}

27.  The half-life of an element is 200 years.  If 3 kg is present now, how much will be
        present after

        (a)  400 years        (b)  20,000 years            (c)  100 years

28.  If f(x) is an exponential function and f(1) = 4 and f(5) = 10, find f(x).

29.  If $100 is invested at 5% interest per year, how many years will it take to double
       your money?

30.  If $500,000 is invested at 10% for 5 years, how much will the investment be worth
       at the end of that time if it is compounded

        a.  quarterly                b.  monthly                c.  continuously

31.  How many digits are in the number 100¹⁰⁰?

32.  Be able to prove some theorems.

Answers