Worksheet featuring problems on logarithmic and exponential equations, including definitions, inverse operations, and practical scenarios involving population and walking speed.

1) A natural logarithm has base e (approximately 2.718), while a common logarithm has base 10.
2) The inverse of an exponential function is a logarithmic function.
3) The inverse of a logarithmic function is an exponential function.
4) 5 thousand people live in Hartford, Connecticut.
5) ln(2)
6) ln(27)
7) ln(z / x³)
8) ln(x⁴y³)
9) ln(3√x)
10) 1
11) 10
12) 1/2
13) 3
14) 5
15) 0
16) x = log₂(3)
17) x = log₅(81.2)
18) x = log₃(100)
19) x = log₃(45)
20) x = (log₉(66)) / 2
21) x = log₃(4)
22) x = log₃(4) / 2
23) x = (log₂(4) - 1) / 2
24) x = 10
25) x = log₄(43) / 2
26) x = ln(10) - 4
27) x = (ln(10)) / 2
28) x = 21
29) x = log₁₄(36) - 4
30) x = log₁₂(20) + 2
31) x = e⁻³
32) x = (log₂₅(144) - 1) / 2
33) x = (log₂(5) + 4) / 3
34) x = e⁻⁴ / 3
35) x = -12
36) x = 50
37) x = 50
38) x = 4
39) x = 5⁴
40) x = (10² - 50) / 2
41) x = (10⁶)^(1/5) / 2 - 25
42) x = (10⁴ + 2) / 3
43) x = 32
44) x = 2
45) x = (e⁴ + 2) / 3
46) x = 2
47) x = -ln(9) / 4
48) x = (ln(20) + 3) / 2
49) x = 3
50) x = e⁴
51) x = 3
52) x = ln(6)
53) x = (e^(8/7) - 5) / 2
54) x = 1 ± √(e⁴ / 2)
55) x = (e³ + 1) / 8
56) x = 3
57) x = 6
58) x = 18
59) x = 6