【2】logaf(x)=logag(x)⇒f(x)=g(x) 把指数或者对数的底数化成一样的,那么就是幂或真数相等。 【3】af(x)=bg(x)⇒f(x)lna=g(x)lnb 如果底不相同,那么通过两边取对数,把幂拿下来进行运算。 【4】a◻2+b◻+c=0 其中◻可能为ax,logax,通过整体代换转化为一元二...
4.5-Exponential and Logarithmic Equations指数和对数方程 856 -- 31:22 App 4.1-Exponential Functions指数函数 466 -- 34:09 App 4.6-Modeling with Exponential and Logarithmic Functions指数和对数函数的应用题 764 1 29:23 App 4.3-Logarithmic Functions对数函数 362 1 12:23 App 16-derivative for bases...
Key Equations One-to-one property for exponential functions T b > 0 , b ≠ 1 , = S Definition of a logarithm b≠1b≠1 log (S) = c bc=Sbc=S One-to-one property for logarithmic functionsFor any algebraic expressionsSandTand any positive real numberb, whereb≠1b≠1, ...
将所有包含对数的项移到等式左边。 2xln(2)+4ln(2)−ln(3)=02xln(2)+4ln(2)-ln(3)=0 将所有不包含xx的项移到等式右边。 2xln(2)=−4ln(2)+ln(3)2xln(2)=-4ln(2)+ln(3) 将2xln(2)=−4ln(2)+ln(3)2xln(2)=-4ln(2)+ln(3)中的每一项除以2ln(2)2ln(2)并化简。
Exponential Equations Exponential Equations Solving Equations Solving a Logarithmic Equation Solving a Logarithmic Equation If the logarithms have the same base, set the two functions equal to each other. Example: 5 5 2 5 5 2 2 l o g l o g 9 l o g l o g 9 9 3 3 i s n o t ...
81. Newton’s Law of Cooling states that the temperature T of an object at any time t can be described by the equation T=Ts+(T0−Ts)e−ktT=Ts+(T0−Ts)e−kt, where TsTs is the temperature of the surrounding environment, T0T0 is the initial temperature of the object, an...
Exponential and Logarithmic Functions#Methods of Solving Exponential Equations and Inequalities#Logarithm of both parts of an exponential equation or inequality#Substitution of variables in exponential equations and inequalities#Standard logarithmic equations and inequalities#Finding a multiplicative dependency#Using...
Rewrite into exponential form EX: Solve: ln x = - 1 / 2 log e x = - 1 / 2 e -1/2 = x x = e -1/2 EX: Solve: 2 log 5 3x = 4 log 5 3x = 2 5 2 = 3x 25= 3x 25 / 3 = x x = 25 / 3 0.607 8.333 Solving Logarithmic Equations Solving Logarithmic Equations •...
Chapter 4 – Exponential and Logarithmic Functions Logarithmic Functions Exponential Functions Recall from last class that every exponential function f (x) = a x with a >0 and a 1 is a one- to-one function and therefore has an inverse function. That inverse function is called the logar...
Precalculus Examples 3x=43x=4 Take thenatural logarithmof both sides of theequationto remove thevariablefrom theexponent. ln(3x)=ln(4)ln(3x)=ln(4) ln(3x)ln(3x) xln(3)=ln(4)xln(3)=ln(4) Divideeachterminxln(3)=ln(4)xln(3)=ln(4)byln(3)ln(3)and simplify....