Question

Дано: $log_{36} 8=a$
Найти $log_{16}9$

Answer 1

a=log₃₆8=(3/2)log₆2=3/(2log₂6)=3/(2(log₂2+log₂3))=3/(2(1+log₂3))⇒1+log₂3=3/(2a)⇒log₂3=3/(2a)-1
log₁₆9=(2/4)log₂3=(1/2)(3/(2a)-1)=3/(4a)-1/2=(3-2a)/(4a)