Evaluate log of 4(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.

1/64=1/4

1/64=4(−3)

3. Substitute the power back into the logarithmic expression.

(log_4)(4(−3))

4. Apply the property of logarithms that states (log_b)(bx)=x

(log_4)(4(−3))=−3

Final Answer

(log_4)(1/64)=−3

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