Answer :
To solve the problem of finding the value of [tex]n[/tex] for the expression [tex]\log 8 + \log 5 = \log n[/tex], we can use a fundamental property of logarithms: the product rule.
Logarithmic Product Rule
The product rule of logarithms states:
[tex]\log a + \log b = \log (a \times b)[/tex]
Applying this rule to the expression [tex]\log 8 + \log 5[/tex]:
[tex]\log 8 + \log 5 = \log (8 \times 5)[/tex]
Now, perform the multiplication inside the logarithm:
[tex]8 \times 5 = 40[/tex]
Thus, the expression simplifies to:
[tex]\log 8 + \log 5 = \log 40[/tex]
Therefore, [tex]n = 40[/tex] and the value of [tex]\log n[/tex] is [tex]\log 40[/tex].
The correct answer is option (b) \log 40.