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解-log2^[9^(x-1)-5]=-log2^[3^(x-1)]-2
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解-log2^[9^(x-1)-5]=-log2^[3^(x-1)]-2
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答案和解析
-log2^[9^(x-1)-5]=-log2^[3^(x-1)]-2
-log2^[9^(x-1)-5]=-log2^[3^(x-1)]-log2^4
-log2^[9^(x-1)-5]=-(log2^[3^(x-1)]+log2^4)
-log2^[9^(x-1)-5]=-log2^[3^(x-1)]*4
log2^[9^(x-1)-5]=log2^[3^(x-1)]*4
[9^(x-1)-5]=[3^(x-1)]*4
[3^(x-1)]^2-4*3^(x-1)-5=0
[3^(x-1)-5][3^(x-1)+1]=0
3^(x-1)=5或3^(x-1)=-1
3^(x-1)=-1无解
3^(x-1)=5
x-1=log3^5
x=log3^5+1=log3^15
-log2^[9^(x-1)-5]=-log2^[3^(x-1)]-log2^4
-log2^[9^(x-1)-5]=-(log2^[3^(x-1)]+log2^4)
-log2^[9^(x-1)-5]=-log2^[3^(x-1)]*4
log2^[9^(x-1)-5]=log2^[3^(x-1)]*4
[9^(x-1)-5]=[3^(x-1)]*4
[3^(x-1)]^2-4*3^(x-1)-5=0
[3^(x-1)-5][3^(x-1)+1]=0
3^(x-1)=5或3^(x-1)=-1
3^(x-1)=-1无解
3^(x-1)=5
x-1=log3^5
x=log3^5+1=log3^15
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