解题方法
1 . 已知
,
,现有如下说法:①
;②
;③
.则正确的说法有______ .(横线上填写正确命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb4a2d342b5210b2a7f66c87b92caee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee38aaef3d774f1f3ec9feec48719a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efa8c67c04d16b7e2d20f9fd90264ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ba5f6d6fd74616791ca9634c0ac55d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436bd161a549d55e748a72d95f71ea8c.png)
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名校
2 . (1)请根据对数函数
来指出函数
的基本性质(结论不要求证明),并画出图象;
(2)拉普拉斯称赞对数是一项“使天文学家寿命倍增”的发明.对数可以将大数之间的乘除运算简化为加减运算,请证明:
;
(3)2017年5月23日至27日,围棋世界冠军柯洁与DeepMind公司开发的程序“AlphaGo”进行三局人机对弈,以复杂的围棋来测试人工智能.围棋复杂度的上限约为
,而根据有关资料,可观测宇宙中普通物质的原子总数约为
.甲、乙两个同学都估算了
的近似值,甲认为是
,乙认为是
.现有两种定义:
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792365589995520/1793820237086720/STEM/2c179cd798bc431f94b813641b8a2aec.png?resizew=190)
①若实数
满足
,则称
比
接近
;
②若实数
,且
,满足
,则称
比
接近
;请你任选取其中一种定义来判断哪个同学的近似值更接近
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3808314697be51e2ff72179fb6556374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b8eea00910cad6239a29a85991f925.png)
(2)拉普拉斯称赞对数是一项“使天文学家寿命倍增”的发明.对数可以将大数之间的乘除运算简化为加减运算,请证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8734005d48f1e77eeaebe832058dee.png)
(3)2017年5月23日至27日,围棋世界冠军柯洁与DeepMind公司开发的程序“AlphaGo”进行三局人机对弈,以复杂的围棋来测试人工智能.围棋复杂度的上限约为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f610f3ed73c02ddc0fd21b34d12ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/013492f5b66a5b5b9169222c524474b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584805a70c17d752bbd0def995accc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0b4b553124abf972a92af238b80480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d10e3a8a2bd5a1fd799f8640d31d826d.png)
![](https://img.xkw.com/dksih/QBM/2017/10/10/1792365589995520/1793820237086720/STEM/2c179cd798bc431f94b813641b8a2aec.png?resizew=190)
①若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b782dd2de9c9caa840838cd63d817de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413915a68960106812e6577dedac2f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376218b0e2c4b0bc42f54573c5703a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5892a5def700f49245c7389aae50a68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584805a70c17d752bbd0def995accc.png)
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