To solve the expression involving logarithms, we can break it down step by step. We need to compute:
\[ \log(9.23) + \log(0.00921) - \log(0.05138) \]
Step 1: Calculate the logs
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Calculate \(\log(9.23)\):
- We can use a calculator or logarithm tables to find this value.
- \(\log(9.23) \approx 0.965\)
-
Calculate \(\log(0.00921)\):
- Since \(0.00921 = 9.21 \times 10^{-3}\):
- \(\log(0.00921) = \log(9.21) + \log(10^{-3}) = \log(9.21) - 3\)
- \(\log(9.21) \approx 0.965\) (from the previous calculation)
- Thus, \(\log(0.00921) \approx 0.965 - 3 = -2.035\)
-
Calculate \(\log(0.05138)\):
- Since \(0.05138 = 5.138 \times 10^{-2}\):
- \(\log(0.05138) = \log(5.138) + \log(10^{-2}) = \log(5.138) - 2\)
- \(\log(5.138) \approx 0.712\)
- Thus, \(\log(0.05138) \approx 0.712 - 2 = -1.288\)
Step 2: Substitute values into the main equation
Now substitute the calculated values back into the original equation:
\[ \log(9.23) + \log(0.00921) - \log(0.05138) \]
Substituting our values, we get:
\[ 0.965 + (-2.035) - (-1.288) = 0.965 - 2.035 + 1.288 \]
Step 3: Calculate the result
Calculating the above:
- \(0.965 - 2.035 = -1.07\)
- Now add \(1.288\):
\(-1.07 + 1.288 = 0.218\)
Final Answer:
Thus, the value of \(\log(9.23 \times 0.00921 / 0.05138)\) is approximately \(0.218\).
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