If 10^x = 1.73 and log_10(1730) = 3.2380 (so antilog(0.2380) = 1.73), find x.
Aptitude
Logarithm
Difficulty: Easy
Choose an option
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A1.2380
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B0.2380
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C2.380
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D2.2380
Answer
Correct Answer: 0.2380
Explanation
Introduction / Context:This tests understanding of characteristics and mantissas in common logarithms. If log_10(1730) = 3.2380, the mantissa 0.2380 corresponds to the significant 1.73 because 1730 = 1.73 × 10^3.
Given Data / Assumptions:10^x = 1.73 and log_10(1730) = 3.2380 ⇒ antilog(0.2380) = 1.73.
Concept / Approach:From 10^x = 1.73 it follows directly that x = log_10(1.73). The provided log indicates log_10(1.73) = 0.2380 (mantissa retained).
Step-by-Step Solution:
x = log_10(1.73) = 0.2380Why Other Options Are Wrong:1.2380 and 2.2380 include an added characteristic (×10 or ×100); 2.380 drops a zero and changes scale.
Final Answer:0.2380