you’ve gotten good at solving exponential equations with logs… … but how would you handle...
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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!
Product Property
NMMN bbb logloglog
Quotient Property
NMN
Mbbb logloglog
Power Property
MxM bx
b loglog
To condense: Rewrite as one logarithm
To expand: Rewrite as multiple logarithm
Example 1: Condense the following logarithmic expression.
4log20log 33
Example 2: Condense the following logarithmic expression.
yx 22 loglog3
Example 3: Condense the following logarithmic expressions.
16log4log2log3
9log9log3 62
Example 4: Expand the following logarithmic expression.
y
x5log
Example 5: Condense the following logarithmic expression.
43log r
Example 6: Condense the following logarithmic expressions.
2
3log
y
437log ba
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