Exponential+&+Logarithmic+Functions+-+B3

=Exponential and Logarithmic Functions= An exponential function, is a function in which x is used as an exponent. When the parent exponential function is graphed it creates a upwards sweeping slope.

A logarithmic function is used as another way to write exponents.
In an exponential function you would write x=b^y, whereas in a logarithmic function y=log,base b,(X). for example 1000=10^3, which is equal to 3=log,Base 10, (1000) Logarithm graph is shown below.

What is the general form of an exponential function?
The general form of of an exponential function is f(x)=a^x, where a>0, and a is not equal to 1. The domain of this function is all real numbers.


 * //What is the natural exponential// //function//?**

The natural exponential function is f(x)=e^x; its inverse is the natural logarithmic function, f(x)=lnx. The natural exponential function is like any other exponential function f(x)=a^x; in this case, e is an irrational number with an approximate value of 2.718281828. Likewise, the natural logarithmic function is simply log base e.

The natural exponential function has many useful applications. One being continuos exponential growth/decay, the formula used for this is y=ae^(rt). Another useful application formula is the n per year compunding exponential growth/decay, which has a formula of y=a(1+(r/n))^(nt). Conceptually you can see that annually compunding exponential growth/decay would have a formula of y=a(1+r)^t.

When solving exponential functions invovling y=e^x there are a few ways to go about it, depending on what variables are left open. If there are variables left in e's exponent you can you ln to "cancel out" e and turn the exponent into not an exponent. Once you have gotten rid of all variable in the exponents, r didnt have any to start with, find a calculator with an e button and a ln button, the just "plug n' chug" to find your answer.

//http://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htm//


 * What is e^x? **
 * The system of logarithms has the number called “e” as its base. The term “e” is named after 18th century mathematician Leonhard Euler.
 * e is an irrational value whose approximate decimal value is 2.718281828
 * e^x is called the natural base
 * To indicate the natural logarithm of a number we write “ln”
 * ln(x)= loge^x
 * 1) What number is ln(e)?
 * ln(e)= 1**
 * 1) Write the following in exponential form: y=ln(x)
 * e^y=x**
 * Properties of Logarithms **

// Expand the following using the Properties of Logs: // // (answers in bold) //
 * Four Basic Properties of Logs**

//1. log3(2x)// //2. log3(2x) = **log3(2) + log3(x)**//

//1. log4( 16/x )// //2. log4( 16/x ) = log4(16) – log4(x)// //3. log4(16) = 2// //4. log4( 16/x ) = **2 –** **log4(x)**//

//1. log5(x^3)// //2. log5(x^3) = 3 · log5(x) = **3****log5(x)**//