Question

Evaluate: log₁₀₀(0.01)
1. 1
2. -1
3. 2
4. -2

Answer 1

Correct Answer - Option 2 : -1

Concept used:

If m and n are positive rational numbers, then

log_a(mⁿ) = n.log_am

loga(b) = (log b)/(log a)

Calculation:

loga(b) = (log b)/(log a)

⇒ log100(0.01) = (log 0.01)/(log 100)

⇒ (log 10-2)/(log 102)

⇒ {-2(log 10)}/{2(log 10)}      ----{loga(mn) = n.logam}

⇒ -1

∴ The value of log₁₀₀(0.01) is - 1.

 

If m and n are positive rational numbers, then

loga(mn) = n.logam

log₁₀10 = 1