Evaluate log of 0.1

Problem

(log_)(0.1)

Solution

1. Identify the base of the logarithm. In common mathematical notation, (log_)() without a specified base typically refers to the common logarithm, which is base 10

2. Rewrite the decimal as a fraction. The value 0.1 is equivalent to 1/10

3. Express the fraction as a power of the base. Using the rule of negative exponents, 1/10 can be written as 10(−1)

4. Apply the logarithm power rule, which states that (log_b)(bx)=x

5. Simplify the expression to find the final value.

Final Answer

(log_)(0.1)=−1

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