To four decimal places, the values of and are
andEvaluate each logarithm by applying the appropriate rule or rules from this section. DO NOT
USE A CALCULATOR. See Example 6.
36. 37. 38.
39. 40. 41.
42. 43. 44.
Decide whether each statement is trueor false.See Example 7.
49. 50.
51. 52.
53.Concept Check Refer to the Note following the word statement of the product rule for
logarithms in this section. Now, state the quotient rule in words, replacing “logarithm”
with “exponent.”
54.Explain why the statement for the power rule for logarithms requires that xbe a positive
real number.
55.Concept Check Why can’t we determine a logarithm of 0? (Hint: Think of the defini-
tion of logarithm.)
56.Concept Check Consider the following “proof ” that does not exist.
Since the logarithm of a negative number is not defined, the final step cannot be evalu-
ated, and so log 2 16 does not exist. WHAT WENT WRONG?=log 2 1 - 42 +log 2 1 - 42=log 2 1 - 421 - 42log 2 16log 2 16log 10 10
log 10 100=
1
10
log 10 7
log 10 14=
1
2
log 3 8 +log 31
8
log 6 60 - log 6 10 = 1 = 0log 3 7 +log 3 7 -^1 = 0 log 3 49 +log 3 49 -^1 = 0log 2 18 + 322 =log 2 8 +log 2 32 log 2 164 - 162 =log 2 64 - log 2 16log 10 log 10 95 log 10 2191
9
log 10249 log 10252 log 10 3log 10 log 10 36 log 10 1629
2
log 102
9
log 10 18 log 10 4log 10 2 =0.3010 log 10 9 =0.9542.log 10 2 log 10 9SECTION 10.4 Properties of Logarithms 603
Write each exponential statement in logarithmic form. See Section 10.3.
Write each logarithmic statement in exponential form. See Section 10.3.
- 2310 =
1
3
log 10 0.001=- 3 log 10 1 = 0 log 10