Sample Test

1) Simplify each:
a) 4 ^. 2^-4 = b) (4 ^. 2)^-4 = c) (a^-1 + b^-1)^-2 =

2) Simplify each:

3) Solve the equation: 9^3x = 81^{x + 1}
^{4) The half life of a radioactive isotope
is 7 days. If 5.6 kg are present now, how much will be present in
t days? In 13 days?}

^{5) A bacteria colony triples every 6 days.
The population currently is 5000 bacteria. What will be the population
in 21 days?}

^{6) $1000 is invested at 8% compounded quarterly
for 3 years. How much interest will you receive at the end of the
time period?}

^{7) You invest $3000 at 7% compounded continuously
for 2 years. How much money will be in the account at the end of
the time period?}

8) Solve each log equation:
                 a) Log x = 21

                 b) Log |x| = 15

                 c) Ln (x² - 1) = 3

                 d) Log x = 1.6 (Use calculator and round to hundredths.)

9) Write each log as a single log:

                 a) Log x + log y + 2Log z

                 b) Ln x + Ln y - 3Ln z

10) Simplify each log:

                 a) Ln e⁵ =

                 b) 10^2log4 =

                 c) 10^{1 + log 5} =

11) Solve the equation: Log (x + 2) + Log 5 = 4

12) Graph y = 3^x and y = log₃ x on the same axis.

13) Use a calculator to find Log₇ 58 and round to hundredths place.

14) Solve the equation: 15^{x
+ 1} = 29 and round to hundredths place.

15) How long will it take to double $1000 if invested at 6% compounded monthly?

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