解方程log2(x+14)-log2(x+6)=3-log2(x+2)
问题描述：
解方程log2(x+14)-log2(x+6)=3-log2(x+2)
答
(x+14)/(x+6)=8/(x+2)
x平方+8x-20=0
x=-10 x=2
答
log2(x+14)-log2(x+6)=3-log2(x+2)
》》log2((x+14)(x+2) /(x+6))=3
》》((x+14)(x+2) /(x+6))=8
》》X^2+16X+28=8X+48
》》X^2+8x-20=0
》》X1=-10（舍去）；X2=2.
望采纳。祝学习愉快、、
答
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)