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对数函数y=log 。(a>0且a≠1),其定义域是 x∈(0,+∞),根据性质有如下命题成立: 1.a∈(0,1),且。∈(0,1),则log_ax>0; 2.a∈(0,1),且x∈(1,+∞),则 log_a<0; 3.a∈(1,+∞),且x∈(0,1),则 log_ax<0; 4.a∈(1,+∞),且x∈(1,+∞)测 log_ax>0. 以下所述可归纳为:底数a与真数x在可取值的相同区间中,其对数值为正,否则其值为负。这样一来,对某个对数式很快可判断其值的符号,因此,给某些对数式的比较带来方便。举例如下: 例1 比较下面两个值的大小:
The logarithm function y=log. (a>0 and a≠1), whose domain is x∈(0,+∞). According to its nature, the following propositions hold: 1.a∈(0,1), and. ∈(0,1), then log_ax>0; 2.a∈(0,1), and x∈(1,+∞), then log_a<0; 3.a∈(1,+∞), and x ∈(0,1), then log_ax<0; 4.a∈(1,+∞), and x∈(1,+∞) measures log_ax>0. The following can be summarized as: base a and real x In the same range of possible values, its logarithmic value is positive, otherwise its value is negative. In this way, for a symbol whose logarithm can quickly determine its value, it is convenient for some logarithmic comparisons. Here are some examples: Example 1 Compares the size of the following two values: