三道高一的对数题,一题五分哦~注 这个符号区分底数和N 1.已知log18~9=a,18^b=5,表示log36~45
1个回答
1.18^b=5
b=log18(5)
a=log18(9)
log36(45)=log18(45)/log18(36)
=[log18(5)+log18(9)]/[log18(18)+log18(2)]
=[a+b]/[1+log(18/9)]
=[a+b]/[1+1-a]
=(a+b)/(2-a)
2.log6(27)=a
log6(3^3)=a
log6(3)=a/3
log18(16)=log6(16)/log6(18)
=[4log6(2)]/[log6(6)+log6(3)]
=[4-4log6(3)]/[1+(a/3)]
=[4-4a/3]/[(a+3)/3]
=(12-4a)/(a+3)
3.log7(3)=a,log7(4)=b
log7(378)=log7(3*3*3*2*7)
=3log7(3)+1/2log7(4)+log7(7)
=3a+(b/2)+1
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