Question

（1）求值：lg2•lg50+lg5•lg20-lg100•lg5•lg2；
（2）已知log₇3=a，log₇4=b，求log₄₉48．

Answer 1

（1）原式=lg2•（lg5+1）+lg5•（lg2+1）-2•lg5•lg2
=lg2+lg5
=1
（2）∵log₇3=a，log₇4=b，
∴log4948=

1

2

log7(3×16)=

1

2

(log73+log716)=

1

2

(log73+2log74)
=

1

2

(a+2b)