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log以2为底数,3为对数等于a,3的b次方等于7,求log以12为底数,56为对数
人气:406 ℃ 时间:2019-08-13 05:20:16
解答
log2(3)=a
则有:log3(2)=1/a
由于:3^b=7
则:log3(7)=b
则:log12(56)
利用换底公式:
log12(56)
=log3(56)/log3(12)
=[log3(7)+log3(8)]/[log3(3)+log3(4)]
=[b+log3(2^3)]/[1+log3(2^2)]
=[b+3log3(2)]/[1+2log3(2)]
=[b+3/a]/[1+2/a]
=[ab+3]/[a+2]
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