Simplify/Condense log base 3 of 27x

Problem

(log_3)(27*x)

Solution

1. Identify the logarithmic property for the logarithm of a product, which states (log_b)(M*N)=(log_b)(M)+(log_b)(N)

2. Apply the property to the expression by splitting the product 27*x into two separate logarithms.

(log_3)(27*x)=(log_3)(27)+(log_3)(x)

3. Evaluate the numerical logarithm (log_3)(27) by determining what power 3 must be raised to in order to equal 27

3=27

(log_3)(27)=3

4. Substitute the evaluated value back into the expression to reach the simplest form.

3+(log_3)(x)

Final Answer

(log_3)(27*x)=3+(log_3)(x)

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