Section 16.2 Expanding Logarithms
Exponent Rule | Logarithm Rule |
Add inside, multiply outside | Multiply inside, add outside |
Subtract inside, divide outside | Divide inside, subtract outside |
Multiply inside, exponent outside | Exponent inside, multiply outside |
Example 16.5.
Suppose we want to expand the following log as much as possible:
It may be tempting to bring some of the exponents out, but we can only do that when the exponent is on the entire inside. So, for example, we cannot yet bring down the 5 because right now it's only the exponent on part of the inside (just the
Now, we will want to bring our exponents outside. However, the middle term has a square root instead of an exponent. So, we need to convert
Now we are finally ready to get our answer by bringing down the exponents.
Checkpoint 16.6.
Separate the following as much as possible