If log₁₀7 = a, evaluate log₁₀(1/70).

Concept / Approach

• Use product/quotient rules and the facts: log₁₀10 = 1 and log₁₀1 = 0.

Step-by-step calculation
log₁₀(1/70) = log₁₀1 - log₁₀70= 0 - [log₁₀7 + log₁₀10]= 0 - [a + 1] = -a - 1

Common pitfalls

• Forgetting to include the +1 from log₁₀10.

Final Answer
-a - 1