Expand the Logarithmic Expression log base 6 of 36x

Problem

(log_6)(36*x)

Solution

1. Identify the logarithmic property for multiplication, which states that the log of a product is the sum of the logs: (log_b)(M*N)=(log_b)(M)+(log_b)(N)

2. Apply the property to the expression by splitting the product 36*x into two separate logarithmic terms.

(log_6)(36)+(log_6)(x)

3. Evaluate the numerical term (log_6)(36) by determining what power 6 must be raised to in order to get 36

6=36

⇒(log_6)(36)=2

4. Substitute the simplified value back into the expression.

2+(log_6)(x)

Final Answer

(log_6)(36*x)=2+(log_6)(x)

Want more problems? Check here!