Multiplying logarithms by a constant
When raising a logarithm to a power, you can bring the power out in front as a multiplier:
Example: Evaluate
Section titled “Example: Evaluate ”- Bring the power of 3 to the front:
. because . - So,
. - Answer:
.
Example: Evaluate
Section titled “Example: Evaluate ”- Bring the power of 4 to the front:
. because . - So,
. - Answer:
.
Splitting up a logarithm with a multiplier
Section titled “Splitting up a logarithm with a multiplier”You can also split up a logarithm with a multiplier into a logarithm with an exponent:
Example: Write
Section titled “Example: Write as a single logarithm”- The power will become 4:
. . - So,
. - Answer:
.