Question

If log x = a + b and log y = a – b, express log (x²y) in terms of a and b.

Answer 1

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

Step-wise calculation: 

Using the log rules (log x^m = m log x and log (uv) = log u + log v).

log (x²y) = log (x²) + log y

= 2 × log x + log y

= 2(a + b) + (a – b)

= 2a + 2b + a – b

= 3a + b