If log_10(10x) = 2.7532, find log_10(10000x).

Introduction / Context:Multiplying a positive number by a power of 10 increases its common logarithm by the exponent (the characteristic). This is standard in mantissa–characteristic operations.

Given Data / Assumptions:log_10(10x) = 2.7532 ⇒ log_10(x) = 1.7532.

Concept / Approach:Compute log_10(10000x) = log_10(x) + 4 because 10000 = 10^4.

Step-by-Step Solution:

Final Answer:5.7532