Simplify/Condense log base 2 of 9x

Problem

(log_2)(9*x)

Solution

1. Identify the expression as a single logarithm of a product.

2. Apply the product rule for logarithms, which states (log_b)(M*N)=(log_b)(M)+(log_b)(N)

3. Expand the expression by splitting the product 9⋅x into the sum of two separate logarithms.

4. Evaluate if any terms can be simplified further; since 9 is not a power of 2 (log_2)(9) remains in logarithmic form.

Final Answer

(log_2)(9*x)=(log_2)(9)+(log_2)(x)

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