Genius Trick to Solve This Type of Exponential Equation

本站添加: 2026-05-06

[00:00:00]What we need to do is to look at this power here this exponent and also look at this and see that there's a way we can factorize this one and it will look similar to this. So that's the first step that we're going to take now. So I'm going to write this as 5 raised to the power factorizing this what is common between 2x and 6 is 2.

[00:00:27]So I take two open up brackets then 2x / 2 we are left with X minus 6 / 2 we are left with 3.

[00:00:39]And that will be equal to 7 raised to the power X minus 3.

[00:00:47]So now if you look at the two powers we have X minus 3 here we have X minus 3 here. So that makes it easier for us and then this 5 raised to power 2 we can square it and that will give us 25.

[00:01:01]Raised to the power X minus 3 and that will be equal to 7 raised to the power X minus 3.

[00:01:11][clears throat] So this is where it gets interesting. If you look at this the power here is the same thing as the power here but the base is not the same thing as the base. So there's trouble here or there's a problem here. So the best thing for us to do when we see a conflicting situation like this because normally when powers are equal it's supposed to mean that the bases are also equal. So you don't need to waste your time in a situation like this. What you just need to do is to take the power which is X minus 3 equate it to zero and solve for X. So if I leave my X here and it will equal to this zero I can ignore it this minus 3 if it comes to this side it becomes plus 3.

[00:01:59]So the value of X is equal to 3 and that is the final answer. If you want to check what you just need to do is to see that if you put 3 as the value of X 3 minus 3 is zero 3 minus 3 is zero. So this will be 7 raised to power zero and this will be 25 raised to the power zero. So if you also do the same you see that the two powers are raised to the I mean the two numbers are raised to power zero to exponent zero and that makes them one on both sides. So any number raised to power zero is one. So that makes this one and this side also one. So the only possible situation for a for a problem like this when the bases are different and the powers are the same is to remember that the powers have to be equal to zero and then by the time you solve you obtain the value of your X and that gives you the final answer. Thank you for watching.