Absorbance–transmittance relationships: which of the following expressions relating absorbance (A), transmittance (T), and percent transmittance (%T) is incorrect?

Introduction / Context:
Connecting absorbance with transmittance is essential for interpreting spectrophotometric data and converting between instrument readouts. Multiple algebraically equivalent forms exist.

Given Data / Assumptions:

• Absorbance is defined as A = −log10(T), where T = P / P0.
• %T = 100 * T.
• Logarithms are base 10.

Concept / Approach:
Derive each expression from A = −log10(T) and %T = 100T. Substitution and logarithm rules show their equivalence.

Step-by-Step Solution:
From A = −log10(T) and T = %T / 100 → A = −log10(%T / 100).Use log rules: A = −[log10(%T) − log10(100)] = 2 − log10(%T).Equivalently, A = log10(100 / %T).Also, A = log10(1 / T) by definition.

Verification / Alternative check:
Plug in sample values (e.g., %T = 10%; T = 0.10): A = 1.000 from all forms, confirming equivalence.

Why Other Options Are Wrong:
This is a trick question: options a, b, and c are all correct identities, hence the only consistent choice is “All are correct.”

Common Pitfalls:
Dropping the factor of 100 when switching between T and %T; mixing natural logs with base-10 logs without conversion.

Final Answer:
All are correct.