1、计算log5^35+2log1/2^根号2-log5^1/50-log5^14
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1、计算log5^35+2log1/2^根号2-log5^1/50-log5^14
2、已知log3^7=a,log2^3=b,求log21^28
2、已知log3^7=a,log2^3=b,求log21^28
log5(35)+2log1/2^(√2)-log5(1/50)-log5(14)
=log5(35)-log5(1/50)-log5(14)+log1/2[(√2)²]
=log5(35÷1/50÷14)+log1/2(2)
=log5(125)+log1/2(2)
=log5(5³)+log1/2[1/2^(-1)]
=3-1=2
log21^28=lg28/lg21
=lg(2²×7)/lg(3×7)
=(2lg2+lg7)/(lg3+lg7)
∵log3^7=a,log2^3=b,∴lg7/lg3=a,lg3/lg2=b
∴lg7/lg2=lg7/lg3×lg3/lg2=ab
∴lg7=ablg2=alg3,lg3=blg2
∴原式=(2lg2+ablg2)/(blg2+ablg2)
=2+ab/b+a
=log5(35)-log5(1/50)-log5(14)+log1/2[(√2)²]
=log5(35÷1/50÷14)+log1/2(2)
=log5(125)+log1/2(2)
=log5(5³)+log1/2[1/2^(-1)]
=3-1=2
log21^28=lg28/lg21
=lg(2²×7)/lg(3×7)
=(2lg2+lg7)/(lg3+lg7)
∵log3^7=a,log2^3=b,∴lg7/lg3=a,lg3/lg2=b
∴lg7/lg2=lg7/lg3×lg3/lg2=ab
∴lg7=ablg2=alg3,lg3=blg2
∴原式=(2lg2+ablg2)/(blg2+ablg2)
=2+ab/b+a
对数 log5(35)+2log1/2( 根号2)-log5(1/50)-log5(14)
对数 log5(35)+2log0.5( 根号2)-log5(0.02)-log5(14)
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