If 10^x = 1.73 and log_10(1730) = 3.2380 (so antilog(0.2380) = 1.73), find x.

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:

Why 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