已知log底数为18真数9等于a,18的b次方等于5,则log底为36真数为45用a.b表示为
问题描述:
已知log底数为18真数9等于a,18的b次方等于5,则log底为36真数为45用a.b表示为
写下论证的步骤.
答
∵log18(9)=a,18^b=5
∴log18(5)=b
∴log36(45)=[log18(45)]/[log18(36)]
= [log18(5*9)]/[log18(18*2)]
=[log18(5)+log18(9)]/log18(18)+log18(2)]
=[a+b]/[1+log18(2)]