Evaluate log of 1/1000

Problem

(log_)(1/1000)

Solution

1. Identify the base of the logarithm. Since no base is explicitly written, it is assumed to be the common logarithm with base 10

(log_10)(1/1000)

2. Rewrite the fraction using a power of 10 Since 1000=10 the fraction can be expressed using a negative exponent.

1/1000=10(−3)

3. Substitute the power back into the logarithmic expression.

(log_10)(10(−3))

4. Apply the logarithm property (log_b)(bx)=x

−3

Final Answer

(log_)(1/1000)=−3

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