Evaluate log base 4 of 1/16

Problem

(log_4)(1/16)

Solution

1. Identify the base and the argument of the logarithm. The base is 4 and the argument is 1/16

2. Rewrite the argument as a power of the base. Since 16=4 the fraction can be written using a negative exponent.

3. Apply the property of exponents where 1/(an)=a(−n)

1/16=1/4=4(−2)

4. Substitute the power back into the logarithm.

(log_4)(4(−2))

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

(log_4)(4(−2))=−2

Final Answer

(log_4)(1/16)=−2

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