Evaluate log of 8

Problem

(log_)(8)

Solution

1. Identify the base of the logarithm. In most contexts where a base is not specified, (log_)() refers to the common logarithm with base 10

2. Apply the definition of a logarithm, which states that y=(log_b)(x) is equivalent to by=x

3. Calculate the numerical value using a calculator or log table for (log_10)(8)

4. Alternative interpretation: If the natural logarithm is intended, the value would be ln(8)≈2.079 If the binary logarithm is intended, (log_2)(8)=3 Assuming common logarithm (base 10:

5. Simplify using the power rule (log_)(ab)=b*(log_)(a) Since 8=2 then (log_)(8)=3*(log_)(2)

6. Substitute the approximate value (log_)(2)≈0.30103

7. Multiply to find the final decimal approximation: 3×0.30103=0.90309

Final Answer

(log_)(8)≈0.90309

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