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 the fraction can be written using a negative exponent.

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

1/36=1/6

1/6=6(−2)

4. Substitute the new expression back into the logarithm.

(log_6)(6(−2))

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

(log_6)(6(−2))=−2

Final Answer

(log_6)(1/36)=−2

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