If x = log 0.6, y = log 1.25 and z = log 3 - 2 log 2, then value of (x + y) is equal to

• (a) < 0
• (b) > 0
• (c) > 1
• (d) < 1

To find the value of \(x + y\) where \(x = \log 0.6\) and \(y = \log 1.25\), we can use properties of logarithms. First, let's calculate each logarithm:

Calculating \(x\) and \(y\)

We know:

• \(x = \log 0.6\) is negative because \(0.6 < 1\).
• \(y = \log 1.25\) is positive since \(1.25 > 1\).

Combining \(x\) and \(y\)

Now, we can add \(x\) and \(y\):

Since \(x\) is negative and \(y\) is positive, we need to determine the overall sign of \(x + y\). To do this, we can express \(x + y\) as:

\(x + y = \log 0.6 + \log 1.25 = \log(0.6 \times 1.25)\)

Calculating the Product

Now, calculate \(0.6 \times 1.25\):

• \(0.6 \times 1.25 = 0.75\)

Final Value of \(x + y\)

Thus, we have:

\(x + y = \log 0.75\)

Since \(0.75 < 1\), it follows that \(\log 0.75\) is negative. Therefore, \(x + y < 0\).

Conclusion

The value of \(x + y\) is less than zero, so the correct answer is:

• (a) < 0