Question

Write the expression as a single logarithm: log₄(x²-36) - 4 log₄(x+6) = ?

Answer 1

The expression log₄(x²-36) - 4 log₄(x+6) can be simplified to a single logarithm by using logarithm properties: log₄[(x²-36)/(x+6)°].

Step-by-step explanation:

To simplify the given expression to a single logarithm: log₄(x²-36) - 4 log₄(x+6), we can use the properties of logarithms:

• The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.
• The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.

First, we can rewrite the 2nd term in the expression: 4 log₄(x+6) as log₄((x+6)°).

Then, by using the second property mentioned above, we can combine the two separate logs into one: log₄[(x²-36)/(x+6)°].

Learn more about Logarithm properties