2+3^(x-1)-9^(x-1/2)=0
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![2+3^(x-1)-9^(x-1/2)=0](/uploads/image/z/5916194-26-4.jpg?t=2%2B3%5E%28x-1%29-9%5E%28x-1%2F2%29%3D0)
2+3^(x-1)-9^(x-1/2)=0
2+3^(x-1)-9^(x-1/2)=0
2+3^(x-1)-9^(x-1/2)=0
2+3^(x-1)-9^(x-1/2)=0
2+3^(x)/3-9^(x)/3=0
2+3^(x)/3-((3^(x))^2)/3=0
设t=3^x,则t>0
则2+t/3-(t^2)/3=0
6+t-t^2=0
t1= -2,t2=3
由于t>0
所以t=3
所以x=1