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Logarithms
Logarithms
The logarithm of a number is the number of times
10 must be multiplied by itself to equal that number.
Logarithms
1000 = 10 x 10 x 10
log 1000 = 3
Logarithms
To find the logarithm of a number, count the zeroes.
If the number is in scientific notation,
look at the exponent.
Logarithms
1 = 1 x 100
10 = 1 x 101
100 = 1 x 102
0.1 = 1 x 10-1
0.01 = 1 x 10-2
log 1 = 0
log 10 = 1
log 100 = 2
log 0.1 = -1
log 0.01 = -2
Logarithms
You can multiply two numbers by adding their logarithms.
Logarithms
You can multiply two numbers by adding their logarithms.
100 x 1000 = 100,000
Logarithms
You can multiply two numbers by adding their logarithms.
100 x 1000 = 100,000
2 + 3 = 5
Logarithms
You can multiply two numbers by adding their logarithms.
1 x 108 = 100,000,000
Logarithms
You can multiply two numbers by adding their logarithms.
1 x 108 = 100,000,000
0 + 8 = 8
Logarithms
You can multiply two numbers by adding their logarithms.
2 x 108 = 200,000,000
? + 8 = ?
Logarithms
So what’s the logarithm of 2? You have to look it up.
2 x 108 = 200,000,000
? + 8 = ?
Logarithms
So what’s the logarithm of 2? You have to look it up.
2 x 108 = 200,000,000
0.301 + 8 = 8.301
Logarithms
What if the number is small instead of big?
Logarithms
What if the number is small instead of big?
0.0003 = 3 x 10-4
Logarithms
What if the number is small instead of big?
0.0003 = 3 x 10-4
log 0.0003 = log 3 + log 10-4
Logarithms
What if the number is small instead of big?
0.0003 = 3 x 10-4
log 0.0003 = log 3 + log 10-4
= 0.477 – 4
Logarithms
What if the number is small instead of big?
0.0003 = 3 x 10-4
log 0.0003 = log 3 + log 10-4
= 0.477 – 4
= -3.523
Logarithms
Try a few!
Logarithms
log 103 =
Logarithms
log 103 = 3
Logarithms
log 108 =
Logarithms
log 108 = 8
Logarithms
log 10-10 =
Logarithms
log 10-10 = -10
Logarithms
log 2 =
Logarithms
log 2 = 0.301
Logarithms
log 5.8 =
Logarithms
log 5.8 = 0.763
Logarithms
log 9.2 =
Logarithms
log 9.2 = 0.963
Logarithms
log 4 x 1012 =
Logarithms
log 4 x 1012 = 0.602 + 12
Logarithms
log 4 x 1012 = 0.602 + 12
= 12.602
Logarithms
log 8.3 x 105 =
Logarithms
log 8.3 x 105 = 0.919 + 5
Logarithms
log 8.3 x 105 = 0.919 + 5
= 5.919
Logarithms
log 7.1 x 10-3 =
Logarithms
log 7.1 x 10-3 = 0.851 - 3
Logarithms
log 7.1 x 10-3 = 0.851 - 3
= -2.149
Logarithms
log 4.8 x 10-11 =
Logarithms
log 4.8 x 10-11 = 0.681- 11
Logarithms
log 4.8 x 10-11 = 0.681- 11
= -10.319
pH
pH = -log [H+]pOH = -log [OH-]
pH + pOH = 14
[H+] = 0.0035
What is the pH?
[H+] = 0.00350.0035 = 3.5 x 10-3
[H+] = 0.00350.0035 = 3.5 x 10-3
log 0.0035 = log 3.5 + log 10-3
[H+] = 0.00350.0035 = 3.5 x 10-3
log 0.0035 = log 3.5 + log 10-3
= 0.544 – 3
[H+] = 0.00350.0035 = 3.5 x 10-3
log 0.0035 = log 3.5 + log 10-3
= 0.544 – 3
= –2.456
[H+] = 0.00350.0035 = 3.5 x 10-3
log 0.0035 = log 3.5 + log 10-3
= 0.544 – 3
= –2.456
pH = 2.456
pH = 6.13
What is the [H+]?
pH = 6.13
–pH = –6.13
pH = 6.13
–pH = –6.13
= 0.87 – 7
pH = 6.13
–pH = –6.13
= 0.87 – 7
[H+] = 7.4 x 10-7
pH = 8.7
What is the pOH?
pH = 8.7
pOH = 14 - pH
pH = 8.7
pOH = 14 - pH
= 14 – 8.7
pH = 8.7
pOH = 14 - pH
= 14 – 8.7
= 5.3
pH = 8.7
pOH = 14 - pH
= 14 – 8.7
= 5.3The solution is acidic.
Always Remember:
Always Remember:The molarity of a solution refers to how many moles per liter it has.
Always Remember:The molarity of a solution refers to how many moles per liter it has.
1.0 M = 1.0 mol/L
Always Remember:A strong acid or base dissociates completely in water.
Always Remember:A strong acid or base dissociates completely in water.
1.0 M HCl = 1.0 M H+
Always Remember:A strong acid or base dissociates completely in water.
1.0 M HCl = 1.0 M H+
1.0 M NaOH = 1.0 M OH-
Always Remember:Polyprotic acids have more than one hydrogen.
Always Remember:Polyprotic acids have more than one hydrogen.
1.0 M H2SO4 = 2.0 M H+
Always Remember:Polyprotic acids have more than one hydrogen.
1.0 M H2SO4 = 2.0 M H+
.
Suggested Homework
Page 609 # 18
Page 611 # 19
Page 612 # 20
