Question

解方程log2(x+14)-log2(x+6)=3-log2(x+2)

Answer 1

log2(x+14)-log2(x+6)=3-log2(x+2)

∴log2[(x+14)/(x+6)]=log2[8/(x+2)]

∴(x+14)/(x+6)=8/(x+2)且(x+14)/(x+6)>0,8/(x+2)>0

∴两边同乘以(x+6)(x+2)得 x^2+16x+28=8x+48

化简得 x^2+8x-20=0

∴x=2或x=-10,

带回8/(x+2),发现当x=-10时,8/(x+2)