Adding logarithms

When adding together two logarithms with the same base, it’s equivalent to multiplying the values inside the logarithms:

Adding two logarithms

Example: Evaluate

• Both have the same base of 2.
• Multiply the values inside: .
• So, .
• because .
• Answer: .

Example: Evaluate

• Both have the same base of 10.
• Multiply the values inside: .
• So, .
• because .
• Answer: .

Adding more than two logarithms

We can do exactly the same when we are adding more than two logarithms with the same base - just multiply all the values inside.

Example: Evaluate

• All have the same base of 3.
• Multiply the values inside: .
• So, .
• because .
• Answer: .

Splitting up a logarithm

You can also split up a logarithm into the sum of two logarithms:

Example: write as the sum of an integer and a logarithm

• 1250 can be split into .
• So, .
• because .
• cannot be simplified further.
• So, .
• Answer: .