Вычислите ㏒₆16 если ㏒₁₂27=а

Log₁₂27=log₁₂3³=3log₁₂3 3log₁₂3=a log₁₂3=a/3 1/log₃12=a/3 log₃3*4=3/a log₃3+log₃2²=3/a 1+2log₃2=3/a 2log₃2=3/a-1 log₃2=(3-a)/2a Теперь выразим log₆16 через log₃2. имеем log₆16=log₆2⁴=4log₆2=4/log₂6=4/log₂2*3=4/(log₂2+log₂3)=  4/(1+log₂3) log ₂3=1/log₃2.=2a/(3-a) Тогда  (1+log₂3) =1+ (2a/(3-a))=(3-а+2а)/(3-а)=(а+3)/(3-а).  log₆16=  4/(1+log₂3)=4*(3-а)/(а+3)