方程log2(9^(x-1)+7)=2+log2(3^(x-1)+1)的解?
问题描述：
方程log2(9^(x-1)+7)=2+log2(3^(x-1)+1)的解?
答
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^2t^2-4t+3=0(t-1)(t-3)=0t=1,t=3t=1时,3^(x-1)=1,则有x...