Expand the Logarithmic Expression log base 3 of 81

Problem

(log_3)(81)

Solution

1. Identify the base and the argument of the logarithmic expression.

2. Rewrite the argument 81 as a power of the base 3

81=3

3. Substitute the power back into the logarithmic expression.

(log_3)(3)

4. Apply the power rule for logarithms, which states (log_b)(xp)=p*(log_b)(x)

4*(log_3)(3)

5. Simplify using the property (log_b)(b)=1

4⋅1=4

Final Answer

(log_3)(81)=4

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