How do I express complicated logs as single logarithms?
The process of transforming a complicated log to a single logarithm depends on the question. However, there are some basic rules and methods that are commonly involved.
Here is an example:
Example
Express 2log3x – log3(x + 4) as a single logarithm
Step 1:
Use the power log rule. The coefficient of 2log3x becomes the power.
log3x2 - log3(x+4)
This makes it easier to compare the logs as you have the same coefficient.
Step 2:
Use the log rule that states subtracting two logs in the same base is the same as division. The subtraction outside can be turned into division inside.
log3x2/(x+4)
You can do this because both logs have the same base (3)
Tips:
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Make sure the logs contain the same base
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Revise the basic log rules so you can easily apply them
KL
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