Exponential Equations with Different Bases

Exponential equations with different bases mean we are going to solve the exponential functions with different bases. Normally exponential functions have the base as e. Here we are going to solve the equations other than e. We will see some example problems for exponential functions with different bases. It is better to understand how to work on the different base. If we want to solve the exponential equations we will use the logarithmic values.


Examples for Exponential Equations with Different Bases:

Solve the following equation 3x = 275x + 3

Solution:

The given equation is 3x = 275x + 3

So we get 3x = ((3)3)5x + 3

From this 3x = (3)15x + 9

From the above we can get x = 15x + 9

15x – x = -9

14x = -9

x = `-9 / 14`

Example 2 for exponential equations with different bases:

Solve the following equation 2x = 42x + 4

Solution:

The given equation is 2x = 42x + 4

So we get 2x = ((2)2)2x + 4

From this 2x = (2)4x + 8

From the above we can get x = 4x + 8

4x – x = -8

3x = -8

So x = `-8 / 3`
More Examples for Exponential Equations with Different Bases:

Example 3 for exponential equations with different bases:

Solve the following equation 5x = 125x + 3

Solution:

The given equation is 5x = 125x + 3

So we get 5x = ((5)3) x + 3

From this 5x = (5)3x + 9

From the above we can get x = 3x + 9

3x – x = -9

2x = -9

So x = `-9 / 2`

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Example 4 for exponential equations with different bases:

Solve the following equation 4x = 16x + 4

Solution:

The given equation is 4x = 16x + 4

So we get 4x = ((4)2) x + 4

From this 4x = (4)2x + 4

From the above we can get x = 2x + 4

x – 2x = 4

-x = 4

So x = 4