log3 (2),log3 (2x-1),log3(2x+11),成等差数列,则x的值最后真确答案是log2(7),

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log3 (2),log3 (2x-1),log3(2x+11),成等差数列,则x的值最后真确答案是log2(7),
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log3 (2),log3 (2x-1),log3(2x+11),成等差数列,则x的值最后真确答案是log2(7),
log3 (2),log3 (2x-1),log3(2x+11),成等差数列,则x的值
最后真确答案是log2(7),

log3 (2),log3 (2x-1),log3(2x+11),成等差数列,则x的值最后真确答案是log2(7),
log3 (2),log3 (2x-1),log3(2x+11),成等差数列
2x-1>0
x>1/2
2log3(2x-1)=log3(2)+log3(2x+11)
(2x-1)^2=2(2x+11)
4x^2-8x-21=0
x1=-1.5(舍去)
x2=3.5

log3 (2x-1)-log3 (2)=log3(2x+11)-log3 (2x-1)
2log3 (2x-1) =log3(2x+11)+log3 (2)
(2x-1)^2 =4x+22
解得：(2x-7)(2x+3)=0
x=3.5,x=-1.5

第一 假设所有的东西都等于Y
log3(2)=y
3^Y=2
求Y
log2(2x-1)=y
2^y=2x-1
log3(2x+11)=y
3^y=2x+11
我想是这样吧......

由题可知
log3(2)+log3(2x+11)=2*log3(2x-1)
有 2*log3(2x-1)=log3(2x-1)^2=log3(4x^2-4x+1)
log3(2)+log3(2x+11)=log3(2*(2x+11))=log3(4x+22)
所以 4x^2-4x+1=4x+22
解得 x=-3/2或7/2
注： ^2是平方

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