Question

³log 12 + ³log 15 - ³log 2 - ³log 1/10 = ...

Answer 1

³log 12 + ³log 15 - ³log 2 - ³log 1/10 = 
= ³log 3.4 + ³log 3.5 - ³log 2 - ³log 1/(2.5)
= ³log 3 + ³log 4 + ³log 3 + ³log 5 - ³log 2 - ³log 2⁻¹.5⁻¹    
= ³log 3 + ³log 4 + ³log 3 + ³log 5 - ³log 2 - (³log 2⁻¹+ ³log5⁻¹)
= ³log 3 + ³log 2² + ³log 3 + ³log 5 - ³log 2 -(- ³log 2 - ³log5)
= ³log 3 + 2. ³log 2 + ³log 3 + ³log 5 - ³log 2 + ³log 2 + ³log5
= 1 + (2. ³log 2) + 1 + (2.³log 5)
= 2 + 2.( ³log 2. ³log 5)