Exponential Functions: In indices, sometimes you will see an unknown being the index/power or even the base of a function, in this situation, it is called an exponential Function. For you to solve such equation, you must express both sides to be in the same index or base as the case may be.
Example 1: For instance we have
This falls to be in exponential Functions because we have the unknown as the index which needed to be known. Evaluating this type of Function requires making both sides to be in the same base, that is;
The last thing here now is to cancel the two equal bases thus, bringing the two powers down for the final result.
Example 2: What if we have x⁴ = 16
This can be solved by making both sides to be in the same Index/power.
x⁴ = 2⁴
So the two powers will cancel each other and our x is now equal to 2.
Solution: If you ever find yourself in this type of indices problem, there are some steps to take for you to be able to bring the problem to its knees.
This step is to use multiplication law to expand the first function.
Dividing both sides by the coefficient of the function
At this point we need to make the both sides to have equal bases.
Is to cancel the two bases since they are equal and bring the two powers down for final result.
Now you can see that 3x = 3, dividing both sides by the coefficient of x will definitely give us x = 1.
With all those steps provided above, Intellect solver is now convinced that you can tackle any type of problems coming from Exponential Functions and indices as a whole.