you’ve gotten good at solving exponential equations with logs… … but how would you handle...

PROPERTIES OF LOGARITHMS

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Page 1: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

PROPERTIES OF LOGARITHMS

You’ve gotten good at solving exponential equations with logs…

… but how would you handle something like this?

733 4log2log x

Properties of Logarithms

1. Product Property2. Quotient Property3. Power Property

The log bases must be the same in order to apply these properties!

Page 4: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Product Property

NMMN bbb logloglog

Page 5: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Quotient Property

NMN

Mbbb logloglog

Page 6: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Power Property

MxM bx

b loglog

Page 7: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

To condense: Rewrite as one logarithm

To expand: Rewrite as multiple logarithm

Page 8: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Example 1: Condense the following logarithmic expression.

4log20log 33

Page 9: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Example 2: Condense the following logarithmic expression.

yx 22 loglog3

Page 10: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Example 3: Condense the following logarithmic expressions.

16log4log2log3

9log9log3 62

Page 11: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Example 4: Expand the following logarithmic expression.

x5log

Page 12: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Example 5: Condense the following logarithmic expression.

43log r

Page 13: You’ve gotten good at solving exponential equations with logs… … but how would you handle something like this?

Example 6: Condense the following logarithmic expressions.

3log

437log ba

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