lga+lgb=2lg(a-2b),求log4^(a/b)的值?已知lg2=a,lg7=b求log8^(9.8)的值?

Question

lga+lgb=2 lg(a-2b),求log4^(a/b)的值?
已知 lg2=a ,lg7=b 求log8^(9.8)的值?

Answer 1

1）lga+lgb=2 lg(a-2b),
lgab=lg(a-2b)²
ab=(a-2b)²
a²-5ab+4b²=0
(a/b)²-5(a/b)+4=0
a/b=1或4
∵a>0,b>0,a-2b>0
∴a/b>2
∴a/b=4
∴log4^(a/b)的值为1.
2）log8^(9.8)
=lg9.8/lg8
=(2lg7+lg0.2)/3lg2
=(2lg7+lg2-1)/3lg2
=(2b+a-1)/3a