Question

解方程log2(9^x-5)+2log1/4(3^x-2)=2

Answer 1

log2(9^x -5)+2log(1/4)(3^x -2)=2

2log4(9^x-5)-2log4(3^x -2)=2

log4(9^x -5)-log4(3^x -2)=1

对数有意义,9^x-5>0 3^x-2>0

log4[(9^x -5)/(3^x -2)]=1

(9^x -5)/(3^x -2)=4

(3^x)²-4×3^x +3=0

(3^x -1)(3^x -3)=0

3^x=1(舍去)或3^x=3

3^x=3 9^x-5=3²=9-5=4>0

x=1