对数函数问题log18 9 = a log18 5 =b 则log36 45= 用a b表示?y=log2 (x^2-a
1个回答
log18 (9 ) = a,
即log18 (18/2) = a,
1- log18 (2) = a,log18 (2) =1-a.
log36( 45)= log18 (45)/ log18 (36)
=[ log18 (9 )+ log18 (5)]/[ log18 (18×2)]
=[ log18 (9 )+ log18 (5)]/ [ log18 (18)+ log18 (2)]
=(a+b)/(1+1-a)= (a+b)/(2-a)
y=log2 (x^2-ax-a)由y=log2 (t)与t= x^2-ax-a复合而成,
y=log2 (t)在定义域上单调递增,
所以t= x^2-ax-a在(-√3,+∞)上递增,
该二次函数的对称轴为x=a/2,则a/2≤-√3,a≤-2√3.
并且函数t= x^2-ax-a作为真数,t的最小值必须大于0,
函数t的最小值是x=-√3时取到,3+√3a-a>0,a>(-3-3√3)/2.
综上可知：(-3-3√3)/2
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