Exponents And Logarithms


Exponent is used to describe how many times a number is multiplied by itself. Example 2 * 2 * 2 here 2 is multiplied three times so we can represent it as 23. Here 3 is the exponent of number 2. So we can say that exponent is the power over any real number or variable. Let us see how Exponents and Logarithms are interrelated:

Definition of logarithm says that y = logax if and only if x = ay. So we can say that logarithms are also exponents.
We can calculate exponent over base number using logarithm. Let us take an example to better understand this concept. Assume that we have an equation 2x = 8. In this we have to find the value of 'x' so will take log both sides:

log(2x) = 8,
x log 2 = log 8,
x= 3 log 2
x = 3,
So value of x = 3.

Let us discuss some properties of log:
·         log x is always assumed to log base 10 which means log x = log 10(x).
·         log xy = log x + log y,
·         log x/y = log x – log y,
·         log xy = y log x,
·         e logx = x,

Let us take an example to understand the reverse process. Assume that we have to find out the value of 'x' from equation log3(x) = 5.
Now in order to get value of 'x' we have to undo logarithm so
log3(x) = 5.
We will use 3 as base of both the sides and put the log in the exponent as:
3log3(x) = 35

Now from the property of logarithm we know that a loga(x) = x,
So we can write this equation as x = 35 which is equal to x = 243.

Topics Covered in Exponents And Logarithms

Exponential Function

Exponential functions are basically terminologies in math which are supposed numbers that are called bases raised to some exponent, also called as powers. For instance, function e4 represents an exponential function. With such functions arithmetic operations are possible but we must abide to certain rules for solving them:

First is the addition of ...Read More

Natural Logarithms

Natural logarithm can be defined as logarithm that has base ‘e’, here value of variable ‘e’ denotes transcendental and irrational constants. Its value is approximately equals to 2.718281828. Natural logarithm is commonly written in the form of ln (k), and in some of the cases it can be written as loge (k), if base of ‘e’ is defined as simply log (k). This i...Read More

Math Topics