Subtracting logarithms
When subtracting logarithms with the same base, it’s equivalent to dividing the values inside the logarithms:
Subtracting two logarithms
Section titled “Subtracting two logarithms”Example: Evaluate
Section titled “Example: Evaluate ”- Both have the same base of 4.
- Divide the values inside:
. - So,
. because . - Answer:
.
Example: Evaluate
Section titled “Example: Evaluate ”- Both have the same base of 10.
- Divide the values inside:
. - So,
. because . - Answer:
.
Subtracting more than two logarithms
Section titled “Subtracting more than two logarithms”We can do exactly the same when we are subtracting more than two logarithms with the same base - just divide all the values inside.
Example: Evaluate
Section titled “Example: Evaluate ”- All have the same base of 2.
- Divide the values inside:
. - So,
. because . - Answer:
.
Splitting up a logarithm with subtraction
Section titled “Splitting up a logarithm with subtraction”You can also split up a logarithm into the difference of two logarithms:
This isn’t usually needed, but it’s good to know it works both ways (is bidirectional).