Question

If log₃ {log₃ [log₃ x]} = log₃ 3, then what is the value of x?
1. 3
2. 27
3. 3⁹
4. 3²⁷

Answer 1

Correct Answer - Option 4 : 3²⁷

Concept:

Properties of logarithms:

\(\rm \frac{log a}{logb}=\log_ba\)

(logx)ⁿ = nlogx

\(\rm \log_aa=1\)

 

Calculation:

Here, log3 {log3 [log3 x]} = log3 3

⇒ log3 {log3 [log3 x]} = 1                ....(∵ \(\rm \log_aa=1\))

⇒ {log3 [log3 x]} = 3¹ = 3

⇒ [log3 x] = 3³ = 27

⇒ x = 3²⁷

Hence, option (4) is correct.