lg5乘log根号10 20 (lg2的根号二次方)的平方=

(lg5)^2+lg2*lg50=(lg5)^2+lg2*(lg2+2lg5)=(lg5)^2+2lg5*lg2+(lg2)^2=(lg5+lg2)^2=(lg10)^2=1根号下[(lg5）^2-2

(lg5)^+lg2xlg50=lg5^+lg2x(lg2+2lg5)=lg5^+lg2^+2lg2lg5=(lg5+lg2)^2=(lg10)^2=1

原式=2lg²√2+lg√2×lg5+√(lg²√2-2lg√2+1)=2(0.5lg2)²+0.5lg2×(1-lg2)+1-lg√2=0.5lg²2+0.5

lg2^2+lg2*lg5+lg5=lg2(lg2+lg5)+lg5=lg2(lg2*5)+lg5=lg2*1+lg5=lg2*5=1

(lg2)^2+lg2*lg5+lg5=lg2*(lg2+lg5)+lg5=lg2*lg(2*5)+lg5=lg2+lg5=lg(2*5)=1

[lg5*lg8000(lg2^根三)^2]/(lg600-1/2lg0.036-1/2lg0.1)=[(lg5*(lg83)(√3*lg2)^2]/[lg62-1/2lg(0.036*0.1)]=[

√（log4(√log3(√log2(512))))=√（log4(√log3√(9)))=√（log4(√log3(3)))=√（log4(√1))=√（log4(1))=√0=0

(lg2)^2+lg4lg5+(lg5)^2=（lg2)^2+2lg2lg5+(lg5)^2=（lg2+lg5)^2=2lg10=2

1

（lg5)^2+lg2*lg50=lg5*lg5+lg2*(lg5+lg10)=lg5*lg5+lg2*(lg5+1)=lg5*lg5+lg2*lg5+lg2=lg5(lg5+lg2)+lg2[这一步

125*³√5=5³*³√5=5^(3+1/3)=5^(10/3)所以原式=10/3

原式=lg2(lg2+lg5)+lg5=lg2×1+lg5=lg2+lg5=1

（lg2)^3+3lg2*lg5+(lg5)^3=(lg^32+lg^35)+3lg2*lg5=(lg2+lg5)(lg^22-lg2*lg5+lg^25)+3lg2*lg5=(lg^22-lg2*l

第一题：设log√28=x所以（√2)^x=8即2^(x/2)=8x/2=3即x=6第二题:（lg5）²+lg2×lg50=（lg5）²+lg2(lg5+lg10)=lg5(lg5

lg2+lg5=lg10=1log2(3)乘log3(2)=1lg2+lg5-log2(3)乘log3(2)=0

f(x)=log2(x/2)*log2(√x/2)=1/2[log2(x/2)]^2=1/2[log2(x)-1]^2=1/2[log2(x)]^2-log2(x)+1/2

lg5*lg8000+(lg2^根号下3)^2+lg1/6+lg0.06=lg5*(3+lg8)+(根号下3*lg2)^2+lg0.01=3lg5+3lg5*lg2+3(lg2)^2-2=3lg5+3

原式=lg5(lg10--lg5)+lg(5根号2)^2+lg2(lg10--lg5)=lg5lg2+lg50+lg2lg2=lg5lg2+1+lg5+(lg2)^2=lg2(lg5+lg2)+1+l

144*√12=12^2*12^(1/2)=12^(2+1/2)=12^(5/2)=[(2√3)^2]^(5/2)=(2√3)^5所以真数=[(2√3)^5]^(1/4]=(2√3)^(5/4)所以原

lg5×log(根号下10)20+(lg2^根号2)^2＝lg5×log(10)20^2+(√2lg2)^2=lg5×2(lg2+1)+2(lg2)^2=2(lg5*lg2+lg5+(lg2)^2)再