Exponential Equation Definition

Introduction to exponential equation definition:

In this article we are going to discuss about exponential equation.An equation can be defined as it is a mathematical statement which contains constants, variables,operation symbols and an equal sign (Or) it can be also defined as an expression with an equal sign.For example, x +3  = 6.Here ' x ' is a variable, ' 3,6 ' are constants, ' + ' is an operational symbol and ' = ' is an equal sign.The exponent can be defined as how many times the number is to be used in multiplication.And this is also called as power.

Exponential equation:

Exponential equation is an equation which involves exponential functions of a variable.

Here there are two forms of exponential equations.Those can be shown in below

1) In first form of exponential equation, we will get same base on each side of the equation.When it happens there is a rule that says,If the bases are same then the exponents are also same.

For example, a^x = a^y  then x = y and a > 0 and `a!=1` .Here the bases are same as ' a '.

2) In the second form of exponential equation, we will get different bases on both side of the equation.Thenn there are different types to solve the exponential equation.That can be shown in below.

Type 1:

If the exponent equation is 2^x = 64

Here the value can be written in the form of base 2 as

2^x = 26

Here the bases are same,then exponents are also same

x = 6

Type 2:

If the exponent equation is 3^x = 11

Here the value 11 is not able to write in the form of base 2. So here we have solve the exponent equation using logarithm.

log ( 3x ) = log ( 11 )

x log ( 3 ) = log ( 11 )

x = `(log(11))/(log(3))`

x = 2.813

Now we are going to discuss some problems regarding on to the exponential equation. Having problem with online algebra equation solver keep reading my upcoming posts, i will try to help you.

Example Problems on Exponential Functions:

Ex:1 Solve the exponential equation 7^2x - 5 = 77

Sol:

Given exponential equation is 7^2x - 5 = 77

Here the bases are same,so the exponents are also same then

2x - 5 = 7

Add 5 on both sides

2x - 5 + 5 = 7 + 5

2x = 12

Divide 2 on both sides

`(2x)/(2) = (12) / (2)`

x = 6

Answer: x = 6

Ex:2 Solve the exponent equation 9^2x = 6561

Sol:

Given exponent equation is 9^2x = 6561

Here the value 6561 can be written in the form of base 9 as 94, then

9^2x = 94

Here the bases are same,so exponents are also same,then

2x = 4

Divide 2 on both sides

`(2x)/(2) = 4/2`

x = 2

Answer: x = 2

Practice Problems on Exponential Equations:

1) Solve the exponential equation 24x = 7

Answer: x = 0.702

2) Solve the exponential equation 119x - 7 = 12110

Answer: x = 3