Expand the Logarithmic Expression log of 0.1

Problem

(log_)(0.1)

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

2. Rewrite the decimal 0.1 as a fraction.

0.1=1/10

3. Express the fraction as a power of 10 using the rule for negative exponents.

1/10=10(−1)

4. Apply the power rule for logarithms, which states (log_b)(xp)=p*(log_b)(x)

(log_)(10(−1))=−1*(log_)(10)

5. Simplify the expression using the property (log_b)(b)=1

−1*(1)=−1

Final Answer

(log_)(0.1)=−1

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