方程log2(9^(x-1)+7)=2+log2(3^(x-1)+1)的解?

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方程log2(9^(x-1)+7)=2+log2(3^(x-1)+1)的解?
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方程log2(9^(x-1)+7)=2+log2(3^(x-1)+1)的解?
方程log2(9^(x-1)+7)=2+log2(3^(x-1)+1)的解?

方程log2(9^(x-1)+7)=2+log2(3^(x-1)+1)的解?
log2[9^(x-1) +7]-log2[3^(x-1) +1]=2
即log2{[9^(x-1)+7]/[3^(x-1)+1]}=2
[9^(x-1)+7]/[3^(x-1)+1]=4
9^(x-1)+7=4*3^(x-1)+4
令3^(x-1)=t,则9^(x-1)=t^2
t^2-4t+3=0
(t-1)(t-3)=0
t=1,t=3
t=1时,3^(x-1)=1,则有x=1
t=3时,3^(x-1)=3,则x=2
代入检验,符合.