Solution:
Let log(-3)(-2) = x + iy
Using logarithmic properties:
(x + iy) = loge(-2) / loge(-3)
(x + iy) loge(-3) = loge(-2)
(x + iy) log' 3 + i(2m + 1)πy = log 2 + i(2n + 1)π
By equating real and imaginary parts, we get:
x log 3 - y(2m + 1)π = log 2
y log 3 + x(2m + 1)π = (2n + 1)π
Solving these equations, we obtain:
x = [(2m + 1)(2n + 1)π² + (log 2)(log 3)] / [(log 3)² + (2m + 1)²π²]
y = [log 3(2n + 1)π - (2m + 1)π log 2] / [(log 3)² + (2m + 1)²π²]
Conclusion
Thus, the general value of log(-3)(-2) is given by the above expressions for x and y.
Source: Manonmaniam Sundaranar University, Directorate of Distance & Continuing Education.