3.2.2 What is a logarithm?
Name:
3-67. Use any patterns you see to fill in the missing numbers. Hint: think exponents.
x
y
625
4
1/5
5
125
1
0
−1
0
25
2
1/25
1/2
Express x as a function of y.
3-68. Use the definition of logarithms to answer the following questions.
a) For example, log5 (25) = 2 because 52 = 25. Complete: log5 625 = 4 because …
b) In problem 3-67, you expressed x as a function of y for the table. Now express y as a
function of x.
3-69. Complete. Refer to part (a) of problem 3-67 as needed.
a) log5 625 =
b) log5 125 =
c) log5 25 =
3-70. Logs will work for any base.
Examples: log3 81 = 4 because 34 = 81
log2 32 = 5 because 25 = 32
a) log2 8 = 3 because…
b) log6 1296 = 4 because…
c) log7 (
) = −2 because…
d) log9 3 =
because…
3-71. Each log equation can be rewritten as an exponential equation, and vice versa. Rewrite
each equation in the other form.
y = 7x
log4 x = y
11y = x
WK = B
K = logW B
log1/3 P = Q
3-72. Experiment with your calculator to determine what base the
What base does it use? How do you know for sure?
button on your calculator uses.