Question 10.

Taking $10^x=a$

we get $a+\frac{4}{a}=\frac{81}{2}$

This would give the quadratic equation: $2a^2-81a+8=0$

We want to find the sum of possible values of x, let the value of x be x1 and x2

these would correspond to log a1, and log a2

The sum of log a1 + log a2 would be log (a1 x a2)

From the quadratic equation we got above, we can see that the product of the possible values of a would-be 8/2 = 4

Threfore, the sum of values of x would be log (4) which would be $2\ \log_{10}2$

Therefore, Option A is the correct answer.