Find log_10(0.000001).

Introduction / Context:Negative powers of 10 translate directly to negative common logs, because log_10(10^k) = k for any real k.

Given Data / Assumptions:0.000001 = 10^{−6}.

Concept / Approach:Apply the fundamental log identity log_10(10^k) = k with k = −6.

Step-by-Step Solution:

Verification / Alternative check:Move decimal six places to the right multiplies by 10^6; the log therefore drops by 6.

Why Other Options Are Wrong:6 and ±5 correspond to incorrect exponents.

Common Pitfalls:Confusing the number of zeros; note there are six places after the decimal before the 1.

Final Answer:−6