什么功能满足以下坐标? (0,1)(52,2)(104,4)(156,8)(208,16)(260,32)(312,64)等等?
X÷52 =(ln(y))÷(ln(2))x值是从0,1,2,3,4,5,6开始的52的倍数.y值是从0开始的2的幂,1,2,3,4,5,6,...因此x = 52a a = x÷52其中a =(0,1,2,3,4,5,6,...)而y = 2 ^ a其中a =(0,1,2,3,4,5,6,...)简化a = log_2(y)通过更改基本规则log_a(b)= log_c(b)/(log_c) (a))log_2(y)= ln(y)÷ln(2)我们将c设为e。现在,a = ln(y)÷ln(2)等于表达式x÷52 =(ln(y))÷(ln(2))
156.25的平方根是多少?
Sqrt(156.25)= 25/2 15625 = 5 ^ 6所以156.25 =(5 ^ 6)/ 100 =(5 ^ 6)/(2 ^ 2 * 5 ^ 2)= 5 ^ 4/2 ^ 2如果a, b> = 0,然后sqrt(a / b)= sqrt(a)/ sqrt(b)如果a,b,c> 0则a ^(bc)=(a ^ b)^ c所以sqrt(156.25)= sqrt(5 ^ 4/2 ^ 2)= sqrt(5 ^ 4)/ sqrt(2 ^ 2)= sqrt((5 ^ 2)^ 2)/ sqrt(2 ^ 2)= 5 ^ 2/2 = 25 / 2