25.Use your calculator to find approximations of the following logarithms.
(a)log 356.8 (b)log 35.68 (c)log 3.568
(d)Observe your answers and make a conjecture concerning the decimal values of the
common logarithms of numbers greater than 1 that have the same digits.
26.Let krepresent the number of letters in your last name.
(a)Use your calculator to find log k.
(b)Raise 10 to the power indicated by the number in part (a). What is your result?
(c) Use the concepts of Section 10.1to explain why you obtained the answer you found
in part (b). Would it matter what number you used for kto observe the same result?
Suppose that water from a wetland area is sampled and found to have the given hydronium ion
concentration. Is the wetland a rich fen,a poor fen,or a bog?See Example 2.
Find the pHof the substance with the given hydronium ion concentration. See Example 2.
33.Ammonia, 34.Sodium bicarbonate,
35.Grapes, 36.Tuna,
Find the hydronium ion concentration of the substance with the given pH.See Example 3.
37.Human blood plasma, 7.4 38.Human gastric contents, 2.0
39.Spinach, 5.4 40.Bananas, 4.6
Solve each problem. See Examples 4 and 6.
41.Consumers can now enjoy movies at home
in elaborate home-theater systems. Find the
average decibel level
for each movie with the given intensity I.
(a)Avatar;
(b)Iron Man 2;
(c) Clash of the Titans;
42.The time tin years for an amount increasing at a rate of r(in decimal form) to double is
given by
This is called doubling time.Find the doubling time to the nearest tenth for an invest-
ment at each interest rate.
(a)2% (or 0.02) (b) 5% (or 0.05) (c)8% (or 0.08)
43.The number of years, , since two independently evolving languages split off from a
common ancestral language is approximated by
where ris the percent of words (in decimal form) from the ancestral language common to
both languages now. Find the number of years (to the nearest hundred years) since the
split for each percent of common words.
(a)85% (or 0.85) (b) 35% (or 0.35) (c)10% (or 0.10)
N 1 r 2 =-5000 ln r,
N 1 r 2
t 1 r 2 =
ln 2
ln 11 +r 2
.
6,310,000,000 I 0
1010 I 0
5.012* 1010 I 0
D=10 log a
I
I 0
b
5.0 10 -^5 1.3 10 -^6
2.5 10 -^12 4.0 10 -^9
3.6 10 -^2 2.7 10 -^7 2.5* 10 -^7
3.1 10 -^5 2.5 10 -^5 2.5* 10 -^2
610 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions
