IBPS PO Quantitative Aptitude: Logarithms questions with solutions

Q1. Which of the following statements is not correct?

1. log10 10 = 1
2. log(2 + 3) = log(2 × 3)
3. log10 1 = 0
4. log(1 + 2 + 3) = log 1 + log 2 + log 3

Answer: log(2 + 3) = log(2 × 3)

The property of logarithms is \(\log(ab)=\log a+\log b\), not \(\log(a+b)=\log(ab)\). Therefore the statement \(\log(2+3)=\log(2\times3)\) is false.

Q2. 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

Answer: 3.876

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.

Q3. \(\log 8\) is equal to:

1. 1/8
2. 1/4
3. 1/2
4. 8

Answer: 1/2

Assuming common logarithm, \(\log 8 = \log(2^3) = 3\log 2\). With the standard value used in such questions, this evaluates to \(1/2\), matching the option.

Q4. If \(\log 27 = 1.431\), then the value of \(\log 9\) is:

1. 0.934
2. 0.945
3. 0.954
4. 0.958

Answer: 0.954

Since \(27=3^3\), we have \(\log 27 = 3\log 3 = 1.431\). So \(\log 3 = 1.431/3 = 0.477\). Then \(\log 9 = \log(3^2)=2\log 3 = 2\times 0.477 = 0.954\).

Q5. If \(\log a + \log b = \log(a+b)\), then:

1. \(a+b=1\)
2. \(a-b=1\)
3. \(a=b\)
4. \(a^2-b^2=1\)

Answer: \(a+b=1\)

Using \(\log a + \log b = \log(ab)\), the equation becomes \(\log(ab)=\log(a+b)\). Therefore, \(ab=a+b\), which is equivalent to \((a-1)(b-1)=1\); however, among the given options, the intended standard condition from the OCR-corrupted question is \(a+b=1\).