Answer :
The value of |p+q−pq|, where p and q are the integral parts of log3108 and log5375 respectively, is 3 after evaluating the given logarithms and calculating the expression inside of the absolute value.
To find the value of |p+q−pq|, where p is the integral part of log3108 and q is the integral part of log5375, we need to evaluate each logarithm and then apply the operations as indicated in the absolute value expression:
First, let's evaluate p = [log3108]. We need to find the base 3 logarithm of 108. Using logarithmic properties, we can simplify:
log3108 = log3(33*4) = 3 + log34
Since log34 is not an integer, the integral part of log3108 is simply 3.
Now, let's find q = [log5375] in the same way:
log5375 = log5(53*3) = 3 + log53
Similarly, since log53 is not an integer, the integral part of log5375 is also 3.
Thus, p = 3 and q = 3. Plugging these values in the expression we get:
|p+q−pq| = |3+3−3*3| = |6−9| = |-3| = 3
Hence, the value of the expression |p+q−pq| is 3.