三、指数函数与对数函数 Third, the exponential function and logarithmic functions
[ 定义 ] [Definition] 形如 Shaped like 
的函数称为指数函数 . The function is called exponential function.
当 a = e 时，为书写方便，有时把 When a = e, in order to facilitate the writing, sometimes 
记作 exp x ，把 Denoted by exp x, the 
记作 exp{ f ( x )} ，等等 . Denoted by exp {f (x)}, and the like.
在函数关系式 In the function formula 
中 In 
，若把 x 视为自变量， y 视为因变量，则称 y 是以 a 为底的 x 的对数函数， x 称为真数，记作 If treated as the independent variable x, y regarded as the dependent variable, y is called as a logarithm function of x, x is called the real number, referred to as 
. 指数函数和对数函数互为反函数 . . Exponential and logarithmic functions mutually inverse functions.
[ 函数图形与特征 ] [Function graphics and features]
方程与图形 Equations and graphics |
特 Special 征 Levy |
指数函数 Exponential function | 曲线与 y 轴相交于点 A (0,1). Curve and the y-axis at point A (0,1). 渐近线为 y =0. Asymptote of y = 0. |
对数函数 Logarithmic function
| 曲线与 x 轴相交于点 A (1,0). Curve intersects with the x axis at point A (1,0). 渐近线为 x =0. Asymptote for x = 0. |
[ 指数运算法则 ] [Index algorithm]
[ 对数的性质与运算法则 ] [Nature and algorithms logarithm] 在下面的公式中，假设 a >0 ，同时所遇到的函数都假设是在定义域里讨论的 . In the following formula, assuming a> 0, while the function are assumed to be encountered in the definition domain of discussion.
零与负数没有对数 No zero and negative logarithm
对数恒等式 Logarithmic identities 
换底公式 Bottom change formula 
[ 常用对数与自然对数 ] [Common logarithm of the natural logarithm]
1 o 1 o 常用对数：以 10 为底的对数称为常用对数，记作 Common logarithm: logarithm to the base 10 called the common logarithm, denoted
2 o 2 o 自然对数：以 e =2.718281828459 L 为底的对数称为自然对数，记作 Natural logarithm: logarithm of e = 2.718281828459 L called for the end of the natural logarithm, denoted
3 o 3 o 常用对数与自然对数的关系： Common logarithm of the natural logarithm of the relationship:
式中 M 称为模数， Where M is called the modulus,
4 o 4 o 常用对数首数求法： Common logarithm method for finding the first few:
若真数大于 1 ，则对数的首数为正数或零，其值比整数位数少 1. If that number is greater than 1, then for the first few numbers of positive or zero, its value is less than the integer digits 1.
若真数小于 1 ，则对数的首数为负数，其绝对值等于真数首位有效数字前面“ 0 ”的个数 ( 包括小数点前的那个“ 0 ” ). If that number is less than 1, then for the first count is negative, its absolute value is equal to the true number of significant figures in front of the first "0" number (including the decimal point in front of the "0").
对数的尾数由对数表查出 . Logarithmic mantissa detected by logarithmic tables.