3-3 Properties of Logarithms
Express each logarithm in terms of ln 2 and ln 5.
1. ln
SOLUTION: 3. ln 80
SOLUTION: 5. ln
SOLUTION: 7. ln 2000
SOLUTION: Express each logarithm in terms of ln 3 and ln 7.
9. ln 63
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11. ln
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3-3 Properties of Logarithms
11. ln
SOLUTION: 13. ln 1323
SOLUTION: 15. ln
SOLUTION: 17. CHEMISTRY The ionization constant of water Kw is the product of the concentrations of hydrogen (H+) and
–
hydroxide (OH ) ions.
+
–
The formula for the ionization constant of water is Kw = [H ][OH ], where the brackets denote concentration in
moles per liter.
a. Express log Kw in terms of log [H+] and log [OH–].
b. The value of the constant Kw is 1 Í 10–14. Simplify your equation from part a to reflect the numerical value of Kw.
c. If the concentration of hydrogen ions in a sample of water is 1 Í 10–9 moles per liter, what is the concentration of
hydroxide ions?
SOLUTION: a.
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3-3 Properties of Logarithms
17. CHEMISTRY The ionization constant of water Kw is the product of the concentrations of hydrogen (H+) and
–
hydroxide (OH ) ions.
+
–
The formula for the ionization constant of water is Kw = [H ][OH ], where the brackets denote concentration in
moles per liter.
a. Express log Kw in terms of log [H+] and log [OH–].
b. The value of the constant Kw is 1 Í 10–14. Simplify your equation from part a to reflect the numerical value of Kw.
c. If the concentration of hydrogen ions in a sample of water is 1 Í 10–9 moles per liter, what is the concentration of
hydroxide ions?
SOLUTION: a.
b.
c.
Evaluate each logarithm.
19. SOLUTION: eSolutions Manual - Powered by Cognero
21. 9 ln e3 + 4 ln e5
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3-3 Properties of Logarithms
Evaluate each logarithm.
19. SOLUTION: 21. 9 ln e3 + 4 ln e5
SOLUTION: 23. 2 log
SOLUTION: 25. 4 log2
SOLUTION: 27. SOLUTION: eSolutions Manual - Powered by Cognero
Expand each expression.
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3-3 Properties of Logarithms
27. SOLUTION: Expand each expression.
29. log9 6x3y 5z
SOLUTION: 31. SOLUTION: 33. log11 ab−4c12d 7
SOLUTION: 35. log4 10t2uv−3
SOLUTION: 37. SOLUTION: eSolutions Manual - Powered by Cognero
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SOLUTION: 3-3 Properties of Logarithms
37. SOLUTION: Condense each expression.
39. SOLUTION: 41. 7 log3 a + log3 b – 2 log3 (8c)
SOLUTION: 43. 2 log8 (9x) – log8 (2x – 5)
SOLUTION: 45. 2 log6 (5a) + log6 b + 7 log6 c
SOLUTION: 47. Manual - Powered by Cognero
eSolutions
SOLUTION: Page 6
SOLUTION: 3-3 Properties of Logarithms
47. SOLUTION: eSolutions Manual - Powered by Cognero
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