Activity Sheet 17
1 – 5. Graph each of the following logarithmic functions.
1.
f  x   log3 x
2.
f  x   log3  x  1
3.
f  x   1  log3 x
4.
f  x    log3 x
5.
f  x   1  log3 x
6 – 9. Write each equation in its equivalent exponential form.
6.
log3  x 1  2
7.
log5  x  4  2
8.
log 4 x  3
9.
log 64 x 
2
3
10 – 13. Evaluate each expression without using a calculator.
10.
log3  log7 7 
11.
log5  log 2 32 
12.
log2  log3 81
13.
log  ln e 
14 – 23. Solve each exponenti9al equation by expressing each side as a power of the same base
and then equating exponents.
14.
2 x  64
15.
5x  125
16.
22 x1  32
17.
42 x1  64
18.
32 x  8
19.
31 x 
1
27
20.
6 x3  6
21.
4x 
1
2
22.
8x 3  16 x 1
23.
e x 1 
1
e
24 – 33. Solve each exponential equation. Express the solution in terms of natural logarithms.
Then use a calculator to obtain a decimal approximation, correct to two places after the decimal.
24.
10 x  3.91
25.
e x  5.7
26.
5 x  17
27.
5e x  23
28.
3e5 x  1977
29.
e15 x  793
30.
e5 x 3  2  10, 476
31.
7 x 2  410
32.
7 0.3 x  813
33.
52 x 3  3x 1
34 – 53. Solve each logarithmic equation. Be sure to reject any value of x that is not in the
domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
use a calculator to obtain a decimal approximation, correct to two places after the decimal, for
the solution.
34.
log3 x  4
35.
ln x  2
36.
log 4  x  5  3
37.
log3  x  4  3
38.
log 4  3x  2   3
39.
5ln 2x  20
40.
6  2ln x  10
41.
ln x  3  1
42.
log5 x  log5  4 x 1  1
43.
log3  x  5  log3  x  3  2
44.
log2  x  2  log2  x  5  3
45.
log4  x  2  log4  x 1  1
46.
2log3  x  4  log3 9  2
47.
3log2  x 1  6  log2 8
48.
log  5x  1  log x  log 4
49.
2 log x  log 25
50.
log  x  4  log 2  log 5x  1
51.
log x  log  x  3  log10
52.
log  x  3  log  x  2  log14
53.
2 log x  log 7  log112