Expand the Logarithmic Expression log base 8 of 9x

Problem

(log_8)(9*x)

Solution

1. Identify the logarithmic property for the product of two terms. The product rule for logarithms states that (log_b)(M*N)=(log_b)(M)+(log_b)(N)

2. Apply the product rule to the expression by treating 9 as M and x as N

3. Expand the expression into the sum of two separate logarithms with the same base.

Final Answer

(log_8)(9*x)=(log_8)(9)+(log_8)(x)

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