Logarithms. The logarithm of a number is the number of times 10 must be multiplied by itself to equal that number.

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Presentation transcript:

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 = 1 x = 1 x = 1 x = 1 x 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, = 5

Logarithms You can multiply two numbers by adding their logarithms. 1 x 10 8 = 100,000,000

Logarithms You can multiply two numbers by adding their logarithms. 1 x 10 8 = 100,000, = 8

Logarithms You can multiply two numbers by adding their logarithms. 2 x 10 8 = 200,000,000 ? + 8 = ?

Logarithms So what’s the logarithm of 2? You have to look it up. 2 x 10 8 = 200,000,000 ? + 8 = ?

Logarithms So what’s the logarithm of 2? You have to look it up. 2 x 10 8 = 200,000, = 8.301

Logarithms What if the number is small instead of big?

Logarithms What if the number is small instead of big? = 3 x 10 -4

Logarithms What if the number is small instead of big? = 3 x log = log 3 + log 10 -4

Logarithms What if the number is small instead of big? = 3 x log = log 3 + log = – 4

Logarithms What if the number is small instead of big? = 3 x log = log 3 + log = – 4 =

Logarithms Try a few!

Logarithms log 10 3 =

Logarithms log 10 3 = 3

Logarithms log 10 8 =

Logarithms log 10 8 = 8

Logarithms log =

Logarithms log = -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 =

Logarithms log 4 x =

Logarithms log 4 x = =

Logarithms log 8.3 x 10 5 =

Logarithms log 8.3 x 10 5 =

Logarithms log 8.3 x 10 5 = = 5.919

Logarithms log 7.1 x =

Logarithms log 7.1 x =

Logarithms log 7.1 x = =

Logarithms log 4.8 x =

Logarithms log 4.8 x =

Logarithms log 4.8 x = =

pH pH = -log [H + ] pOH = -log [OH - ] pH + pOH = 14

[H + ] = What is the pH?

[H + ] = = 3.5 x 10 -3

[H + ] = = 3.5 x log = log log 10 -3

[H + ] = = 3.5 x log = log log = – 3

[H + ] = = 3.5 x log = log log = – 3 = –2.456

[H + ] = = 3.5 x log = log log = – 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 = 5.3 The solution is acidic.

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 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 H 2 SO 4 = 2.0 M H +

Always Remember: Polyprotic acids have more than one hydrogen. 1.0 M H 2 SO 4 = 2.0 M H +.

Suggested Homework Page 609 # 18 Page 611 # 19 Page 612 # 20