Question

解方程log4(3*2^x+7)=log2(2^x+1)

Answer 1

log4(3*2^x+7)=log2(2^x+1)

lg(3*2^x+7)/lg4=lg﹙2^x+1)/lg2

lg(3*2^x+7)/2lg2=lg﹙2^x+1)/lg2

lg(3*2^x+7)/2=lg﹙2^x+1)

√﹙3*2^x+7﹚=2^x+1

3*2^x+7=﹙2^x+1﹚²

3*2^x+7=﹙2^x﹚²＋2×2^x＋1

﹙2^x﹚²－1×2^x－6=0

﹙2^x－3﹚﹙2^x＋2﹚=0

∴2^x=3

x=log2底3