1.

If log3 {log3 [log3 x]} = log3 3, then what is the value of x?1. 32. 273. 394. 327

Answer» 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.


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