Evaluate log base 4 of 1/64

Problem

(log_4)(1/64)

Solution

1. Identify the base and the argument of the logarithm. The base is 4 and the argument is 1/64

2. Rewrite the argument as a power of the base. Since 64=4 the fraction can be written using a negative exponent.

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

1/64=1/4=4(−3)

4. Substitute the power back into the logarithm.

(log_4)(4(−3))

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

−3

Final Answer

(log_4)(1/64)=−3

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