Evaluate log base 12 of 1/144

Problem

(log_12)(1/144)

Solution

1. Identify the base and the argument of the logarithm. The base is 12 and the argument is 1/144

2. Rewrite the argument as a power of the base. Since 144=12 the fraction can be written using a negative exponent.

1/144=1/12

1/12=12(−2)

3. Apply the property of logarithms (log_b)(bx)=x

(log_12)(12(−2))=−2

Final Answer

(log_12)(1/144)=−2

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