The difference between the logarithms of sum of the square of two positive numbers A and B and the sum of logarithms of the individual numbers is a constant C. If A = B, then C is

I think he first case is only possible when A=B=1. So C should be 0.

A B C started a business and invested in the ratio of 3:4:5 After 4 months A withdraw 1/12 of amount of what B and C invested. If the total income was 9200 the what was the share of B?

Assuming the income was for one year, the share of B should be 3200. My thinking behind this was that A invested 3x amount for 4 months and 3x - 9x/12 for the last 8 months while B and C invested 4x and 5x for the full 12 months. Using the same to calculate the ratio, 4x*12/(3x*4 + (3x-9x/12)*8 + 4x*12 + 5x*12) and multiplying the ratio by 9200, we will get 3200.