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2^(2+log2 3)+3^(2%log3 9)

2^(2+log2 3)+3^(2-log3 9) =2^2*2^(log2 3)+3^2/3^(log3 9) =4*3+9/9 =12+1 =13

2log₃ 2-log₃(32/9)+log₃8-3^(2+log₃5) =log₃4-log₃(32/9)+log₃8-3^2*3^log₃5 =log₃(4÷32/9×8) -9*5 =log₃(4×9/32×8)-45 =log₃9-45 =2-45 =-43 最后的式子指数应该加括号,...

(log3∧2+log9∧2)×(log4∧3+log8∧3)=(log3∧2+log(3^2)∧2)×(log(2^2)∧3+log(2^3)∧3)=(log3∧2+1/2log3∧2)×(1/2log2∧3+1/3log2∧3)=3/2log3^2*5/6log2^3=5/4

原式=(1/2*log2^3+1/3*log2^3)(log3^2+1/2*log3^2) =(5/6*log2^3) * (3/2*log3^2) ={5/6*(lg3)/(lg2)} * {3/2*(lg2/lg3)} =5/4 答案对吗??我很久没做这种题了 ~~~

log4(√3+2)^2=log2(√3+2),log9(√3-2)^2=log3(√3-2)。 2^log4(√3+2)^2+3^log9(√3-2)^2 =2^log2(√3+2)+3^log3(√3-2) =(√3+2)+(√3-2) =2√3

(log2^3+log4^9)(log3^4+log9^2)= (3*log2+18*log2)(4*log3+4*log3)= 21*log2*8*log3=168log5

不知道是不是图片上的这个意思。

(log3 2+log9 2)*(log4 3+log8 3) =(lg2/lg3+lg2/lg9)*(lg3/lg4+lg3/lg8) =(lg2/lg3+lg2/2lg3)*(lg3/2lg2+lg3/3lg2 =3/2*lg2/lg3*5/6*lg3/lg2 =3/2*5/6=5/4

对数连底都没有!!!

(log3 2+log9 2)*(log4 3+log8 3) =(lg2/lg3+lg2/lg9)*(lg3/lg4+lg3/lg8) =(lg2/lg3+lg2/2lg3)*(lg3/2lg2+lg3/3lg2 =3/2*lg2/lg3*5/6*lg3/lg2 =3/2*5/6=5/4

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