Exponential Equations

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Exponential equations are basically the tool which is helpful in evaluating the values of unknown variables which are generally in powers. This tool is helpful in evaluating the exponential equations either by comparison method or by taking the logarithmic function in both sides of the equation.  This tool eases the calculation steps and hence it easily evaluates the value of unknown variable in exponent or we can say in power. The above concept can be better clarified by taking the suitable examples and the examples are shown below. In this case, for better understanding we will take both the cases that is one of comparison in case of same base and logarithmic method in case of different base.

Question 1:- Find x if 3^ (4x) = 27^ (x+1)

Solution 1:- Given 3^ (4x) = 27 ^ (x+1)

This further implies,

3 ^ (4x) = 3^ (3x+3)

Since bases are equal on both sides, it means that its power must also be same.


4x = 3x + 3

On solving, we get

4x – 3x = 3

Hence x = 3

Question 2:- Find x if 5^x = 10

Solution 2:-Given 5^ x = 10

Since bases are not same, so in this case we need to apply log both sides,

Therefore log 5^x = log 10

So x log 5 = log 10

Therefore, x = log 10/log5

By writing down the values of log 10 and log 5, we can easily evaluate the actual value of x.

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