Simplify/Condense log base 3 of 81x

Problem

(log_3)(81*x)

Solution

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

2. Apply the property to split the expression into two separate logarithms.

(log_3)(81*x)=(log_3)(81)+(log_3)(x)

3. Evaluate the numerical logarithm by identifying that 81 is a power of 3

81=3

4. Simplify the term (log_3)(3) using the property (log_b)(by)=y

(log_3)(3)=4

5. Combine the results to write the final simplified expression.

4+(log_3)(x)

Final Answer

(log_3)(81*x)=4+(log_3)(x)

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