Question

If log x = 3a + 2b and log y = 2a – b, express log (x³y²) in terms of a and b.

Answer 1

Given: log x = 3a + 2b and log y = 2a – b

Step-wise calculation:

log(x³y²) = 3 × log x + 2 × log y

= 3(3a + 2b) + 2(2a – b)

= 9a + 6b + 4a – 2b

= 13a + 4b