Logarithmic Functions
1. Change the equations written in
logarithmic form into exponential form.
| a) | log28 = 3 | d) | log 1000 = 3 |
| b) | |
e) | ln 6 = 1.7917... |
| c) | |
f) | log2(2x+3) = 3y - 5 |
2. Find the number by using exponential form.
| a) | log232 | c) | ln e5 | e) |  |
| b) |  |
d) | log7 1 | f) | loga ax |
3. Change the equations written in
exponential form into logarithmic form.
| a) | 43 = 64 | c) | ec = b |
| b) |  |
d) | 10- 2 = .01 |
4. Solve for x . Suggestion: Rewrite
the equation in logarithmic form..
| a) | 2 a x = 5 | c) | 3 e x+2 = 7 |
| b) | a 2x + 3 = b+1 | d) |  |
5. Solve the x.Suggestion:
Rewrite each equation in exponential form.
| a) |  |
c) | ln x3 = 12 |
| b) | log x2 = 4 | d) | log 5 (3-2x) = -2 |
6. Simplify the expression a logax.
{Suggestion:
Let y = a logax.
Rewrite this equation in log form
and then find y.}
7. Use a calculator to evaluate the following logarithms
and record the answer to at least 4 decimal places of accuracy.
| a) |  |
c) |  |
| b) |  |
d) |  |
8. The population P(t) of India may be
approximated
by the formula P(t) = 825 e .022t , where t is the number
of
years after 1990 and the population is measured in millions.
a) Using this model, find the population of India in the year 1996.
b) Find the year when the populaton will reach 1 billion.
9. The air pressure p(h) (in lb/in2 ) at an
altitude of h feet above sea level
may be approximated by p(h) = 14.7 e -.0000385
h.
a) Using this model, find the air pressure at the summit of a mountain 20,000 ft.
b) Using this model, find the air pressure in a
valley 1000 ft below sea level.
c) At what altitude will the air pressure be 12 lb/in2 ?