1.hurt和injure到底有什么区别啊,我觉得都差不多么,老师说hurt表示肉体伤害,可是injure也可以吧.求讲

1.hurt和injure到底有什么区别啊,我觉得都差不多么,老师说hurt表示肉体伤害,可是injure也可以吧.求讲解.
2.believe和believe in有什么区别.
3.log(0.5)x【就是以0.5为底,x的对数】＞0.5 这个怎么解?

1.从理论上面说是可以互换的
你可以看一下讲解
Hurt, injure的区别:
首先,两都都可以表示因某某事受伤,或被某某物体或某某人所伤,即指物理伤害.
其次,两都都可以用来表示 情感方面的伤害.
因此,两者可以互换.
区别在於, Hurt即可作动词,又可作名词用,而injure只能作动词用.它的名词形式为injury.
例句:
My leg hurts.
我的腿受伤了.
I hurt it playing football.
我踢足球时伤著它的.
Many people were hurt when the a bus and a truck collided.
一辆公交和一辆货车相撞,许多人受伤了.
She's hurt because you haven't visited her.
她很伤心,因为你没有去看她.
I was very much hurt at his words.
他的话伤透了我的心.
You'll hurt her feelings if you forget her birthday.
如果你忘了她的生日,那会伤她感情的.
There were two people injured in the car accident.
有两个人在车祸中受了伤.
She was injured badly in an accident during the work.
她在一次工伤事故中受了伤.
She injures a man's pride
她伤了男人的自尊心.
2.believe是相信的意思,针对某件具体的事情
believe in是信任的意思,针对某人的总体.另外,believe in还可以翻译为“信仰”等等类似含义.
I believe in you, but I don't believe you this time. 我对你是信任的,但这件事情上面,我不信你说的.
I really can't believe that he would do me such a favor. Since last time I was cheated by him, I no longer believe in him at all.
我实在不相信他会帮我这个忙.自从上次给他骗过之后,我再也不信任他了.
有一些重要补充,尤其是对于believe in的用法:
简单的说
就是believe强调对事不对人,believe somebody或something, 强调的是相信事情的真实性,或者强调某人说的话的真实性,总的就是客观地对事情而言的.
但此外,believe还可以表示有宗教信仰(此时是不及物动词) 如"He thinks that everyone who believes will go to heaven"他认为凡是信神者都能进天堂.
而believe in有许多不同的意思
最常见的,就是楼上几为提到的,是指"信任", 就是对人不对事的, believe in somebody表示对某人信任
但是believe in 还有一些别的意思
如(1): believe in somebody/something可以表示相信某人/某事物的存在
如I believe in God. 不是说"我信任上帝",而是"我相信上帝的存在"
又如 believe in ghost就是相信有鬼的存在
(2): believe in doing something
可以表示认为做某事有用,肯定某事物的价值
如He believes in doing plenty of exercise
指"他相信多做运动有好处"
3.用换底公式
log(M)N=lnN/lnM
log(0.5)x
=lnx/ln0.5>0.5
lnx>0.5*ln0.5
lnx>ln(0.5)^0.5
x>(1/2)^(1/2)即二分之根号二