The Secret Entrance Exam Trick for Exponents

Added: 2026-05-07

[00:00:00]Let me show you how to solve this amazing interesting exponential equation. You will love this. Pay close attention to this. By the end of this video, you will love the solution to this. So, watch this to the end. We have 47 49 to the^ x is = x ^ 14. So, we are asked to find the value of x. Now to solve this we are going to introduce something tricky to this equation which will help us to get our solution very fast and very easy.

[00:00:33]Now what we are going to do is that let us multiply each power by 1 /x that is the reciprocal of x which is 1 /x. Let us multiply that reciprocal of x to both powers and see what we shall have. So we shall have 49 to the^ of x all the power 1 /x is equal to x ^ of 14 all to the power of 1 /x.

[00:01:03]So we observe that if you multiply this x by 1 /x this will cancel out. we shall have 49 to be equal to um x to the power of 14 /x because this 14 * 1 /x is 14 /x. So what next? Let us multiply both power again by the reciproal of 14 which is 1 / 14. So we shall have 49 to the^ of 1 / 14 is = x ^ 14 / x all to the power of 1 / 14. Now look at this.

[00:01:47]This 14 we neutralize this 14 and this 49 can be written as 7^ 2 all to the power of 1 / 14 to be equal to x. Now this neutralize this you left with one which is 1 / x.

[00:02:05]So this two can multiply this 1 / 14. So we shall have 7 ^ 2 / 14 is = x ^ 1 /x 2 is 7 into 14 7 times. So we shall have 7 ^ 1 / 7 is = x ^ 1 /x.

[00:02:25]Now we are going to compare this equation. Comparison means check whether the value of the unknown is correct. So this implies that since 7 is 7 is equal to this or 7 ^ 1 7 is equal to x ^ 1 7. So we can equally say that 1 / 7 is equal to 1 /x. So if you cross multiply you notice that this implies that the value of x is equal to 7. So from the base we observe x is just equal to 7. So that's the final answer. If this video is interesting, help us to share this video to follow and subscribe for more tips like this.