Evaluate log base 6 of 1/36

Problem

(log_6)(1/36)

Solution

1. Identify the base and the argument of the logarithm. The base is 6 and the argument is 1/36

2. Rewrite the argument as a power of the base. Since 36=6^2 the fraction can be written using a negative exponent.

3. Apply the property of exponents 1/(a^n)=a^(−n) to express the argument as 6^(−2)

1/36=1/6^2

1/6^2=6^(−2)

4. Substitute the new expression back into the logarithm.

(log_6)(6^(−2))

5. Apply the logarithm power rule (log_b)(b^x)=x to find the value.

(log_6)(6^(−2))=−2

Final Answer

(log_6)(1/36)=−2

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