Exponential Equation

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Exponential equation is the equation in which the variables are generally in the power. And generally in these type of equations we need to evaluate the variable x. When the base is same then we can easily find the value of variable, because we know that when base are same or equal then its power must also be equal. By equating the power, we can easily find the value of unknown variable, say x easily. Sometimes the bases are not same, then in that case generally we use logarithmic function to evaluate the value of unknown variable, say x. This can be understood by the following examples.

Question 1:- Find the value of x if 2 ^ (2x+4) = 2 ^ (x+8)

Solution 1:- Given 2^ (2x+4) = 2^ (x+8)

The base is 2 on both sides that mean, base are equal on both sides.

We know that When base are equal on both sides, then its exponents are also equal.

Therefore,

2x+4 = x+8

Subtract 4 both sides of the equation,

2x+4-4 = x+8-4

2x = x+ 4

So 2x – x = 4

Hence x = 4
 
Question 2:-Find the value of x if 2 ^ (3x+4) = 4 ^ (x+8)

Solution 2:-Given 2^ (3x+4) = 4^ (x+8)

Therefore, 2^ (3x+4) = 2^2(x+8)

So 2^ (3x+4) = 2^ (2x+16)

The base is 2 on both sides that mean, base are equal on both sides.

We know that When base are equal on both sides, then its exponents are also equal.

So 3x +4 = 2x+16

So by solving,

3x – 2x = 16-4

So x = 12.s

 

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