Evaluate log base 6 of 216

Problem

(log_6)(216)

Solution

1. Identify the base and the argument of the logarithm. The base is 6 and the argument is 216

2. Rewrite the argument 216 as a power of the base 6

3. Calculate the powers of 6 6^1=6 6^2=36 and 6^3=216

4. Substitute 6^3 for 216 in the logarithmic expression.

5. Apply the logarithm property (log_b)(b^x)=x to simplify the expression.

Final Answer

(log_6)(216)=3

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