Exams › IBPS PO › Quantitative Aptitude

If \(\log 2 = 0.3010\) and \(\log 3 = 0.4771\), the value of \(\log_{5} 512\) is:

1. 2.870
2. 2.967
3. 3.876
4. 3.912

Correct answer: 3.876

Solution

Using change of base, \(\log_5 512 = \frac{\log 512}{\log 5}\). Since \(512 = 2^9\), \(\log 512 = 9\log 2 = 2.709\), and \(\log 5 = \log(10/2)=1-0.3010=0.6990\). Dividing gives approximately 3.876.

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