Evaluate log of 1/100

Problem

(log_)(1/100)

Solution

1. Identify the base of the logarithm. Since no base is specified, we assume the common logarithm with base 10

2. Rewrite the fraction as a power of 10 Since 100=10 the fraction 1/100 can be written using a negative exponent.

1/100=10(−2)

3. Substitute the power back into the logarithmic expression.

(log_10)(10(−2))

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

(log_10)(10(−2))=−2

Final Answer

(log_)(1/100)=−2

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