作业帮[(lg3)^2-(lg2)^2]÷(lg9-lg4)+log下面是2上面是根号2,等于多少饿
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![[(lg3)^2-(lg2)^2]÷(lg9-lg4)+log下面是2上面是根号2,等于多少饿](/uploads/image/z/10229752-64-2.jpg?t=%5B%28lg3%29%5E2-%28lg2%29%5E2%5D%C3%B7%28lg9-lg4%29%2Blog%E4%B8%8B%E9%9D%A2%E6%98%AF2%E4%B8%8A%E9%9D%A2%E6%98%AF%E6%A0%B9%E5%8F%B72%2C%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%E9%A5%BF)
[(lg3)^2-(lg2)^2]÷(lg9-lg4)+log下面是2上面是根号2,等于多少饿
[(lg3)^2-(lg2)^2]÷(lg9-lg4)+log下面是2上面是根号2,等于多少饿
[(lg3)^2-(lg2)^2]÷(lg9-lg4)+log下面是2上面是根号2,等于多少饿
[(lg3)^2-(lg2)^2]÷(lg9-lg4)
=(lg3+lg2)(lg3-lg2)÷(2lg3-2lg2)
=(lg3+lg2)(lg3-lg2)÷2(lg3-lg2)
=(lg3+lg2)/2
log下面是2上面是根号2=lg2^(1/2)/lg2=1/2
原式=(lg3+lg2)/2+1/2=1/2(1+lg6)=1/2(lg60)
0.5lg6+1/2
原式=(lg3+lg2)lg3/2÷(1/2)lg3/2+1/2
=(1/2)lg6+1/2
[(lg3)^2-(lg2)^2]÷(lg9-lg4)+log2(√2)
=(lg3+lg2)(lg3-lg2)÷(lg9/4)+1/2
=(lg3+lg2)(lg3-lg2)÷2(lg3/2)+1/2
=lg6*lg3/2÷2(lg3/2)+1/2
=1/2lg6+1/2
=1/2(lg6+1)
(lg3)^2-(lg2)^2=（lg3+lg2）（lg3-lg2）=lg(3*2)lg(3/2)=lg6*lg(3/2)
lg9-lg4=lg(9/4)=lg(3^2/2^2)=2lg(3/2)
所以： [(lg3)^2-(lg2)^2]÷(lg9-lg4)=[lg6*lg(3/2)]/[2lg(3/2)]=(1/2)*lg6=lg根号6
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(lg3)^2-(lg2)^2=（lg3+lg2）（lg3-lg2）=lg(3*2)lg(3/2)=lg6*lg(3/2)
lg9-lg4=lg(9/4)=lg(3^2/2^2)=2lg(3/2)
所以： [(lg3)^2-(lg2)^2]÷(lg9-lg4)=[lg6*lg(3/2)]/[2lg(3/2)]=(1/2)*lg6=lg根号6
log下面是2上面是根号2=log下面是2(2)^(1/2)=1/2。
[(lg3)^2-(lg2)^2]÷(lg9-lg4)+log下面是2上面是根号2=lg根号6+1/2=(1/2)lg60
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