速度求解,一道数学题,第三题。。。
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(1) log12(5)=lg5/lg12
=lg(10/2)/lg(3*2*2)
=(1-lg2)/(lg3+2lg2)
=(1-a)/(b+2a)
(2)运用换底:log14(56)=log3(56)/log3(14)
=〔log3(7)+log3(8)〕/〔log3(7)+log3(2)〕
log3(2)=1/log2(3)=1/a
log3(8)=3log3(2)=3/a
原式=(b+3/a)/(b+1/a)
=(ab+3)/(ab+1)
=1+2/(ab+1)
=lg(10/2)/lg(3*2*2)
=(1-lg2)/(lg3+2lg2)
=(1-a)/(b+2a)
(2)运用换底:log14(56)=log3(56)/log3(14)
=〔log3(7)+log3(8)〕/〔log3(7)+log3(2)〕
log3(2)=1/log2(3)=1/a
log3(8)=3log3(2)=3/a
原式=(b+3/a)/(b+1/a)
=(ab+3)/(ab+1)
=1+2/(ab+1)
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