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