If log a + log b = log(a + b), then which relation holds true?

Given data

• log a + log b = log(a + b)

Concept / Approach

• Use logarithm property: log x + log y = log(xy), for positive x, y (same base).

Step-by-step calculation

log a + log b = log(ab)Given this equals log(a + b)Therefore, ab = a + b (since logarithm is injective on positive reals)ab = a + b

Verification / Notes

Example: a = 2, b = 2 ⇒ ab = 4 and a + b = 4; equality holds and logs match.

Common pitfalls

• Assuming any base or negative values; logs require positive arguments and fixed base.

Final Answer

ab = a + b