Only 10% Students Solve this Exponential Math Olympiad Question | 3^m -2^m =65 |

Hinzugefügt: 2026-05-13

[00:00:00]Hello everyone, welcome to my YouTube channel. Today we are solve a interesting exponential math problem which is 3 to the power mus 2 the power m is equal to 65 m is equal to 5. So how to solve this or interesting maths question or math solution our question which is 3 to the power m - 2 the power m is equal to 65. This is our question.

[00:00:30]Now you can say this is 3 ^ m bracket whole ^ 1 - 2 ^ m bracket whole to the power 1 is equal to 65.

[00:00:46]Now at this moment this expression it will be 3 ^ m bracket this one you can see there is this is 2 / 2 this is 1 minus 2 ^ m then this one it will be 2 / 2 this is 1 is equal to 65.

[00:01:13]Then we know that the exponential formula a to the power m bracket whole to the power n which is a to the power m n I apply this mass formula here. So this expression it will be 3 to the power m over two. I take this two here bracket whole to the power this two. I take this two inside the bracket minus here is same case 2 to the power m / 2 bracket whole to the power this 2 is equal to 65.

[00:01:47]Now this is ^ m / 2. This is 2 the power m / 2. So let 3 to the power m / 2 is equal to x.

[00:02:00]Then 2 to the power m / 2 is = y.

[00:02:06]So I substitute this value here. So this it will be x ^ 2 because of that this is equal to x and this is equal to y. I take this y here. y to the power 2 is equal to 65.

[00:02:21]Then we know that a squar minus b² which is a + b * a minus b. I apply this mass formula here. So which is x + y * x - y = 65.

[00:02:44]A is x and y is a positive integer. Then you can say here x + y is always greater than x - y.

[00:02:55]Now if I find out the factor of 65 so it will be x + y * x - y is equal to this is 13 * 5 13 * 5 this is 65 or you can say 5 * 13 but remember that it is always greater than this. So at this moment uh I can easily here x + y is = 13. If I compare both and x - y = 5 then if I add both I add both so x + this is x but y this is - y so it will be zero but 13 + 5 this is 18.

[00:03:47]Now at this moment if I divide both side by 2 you can say here x = 9. So we find out x = 9. Then again if I take this value again here x + y = 13 x - y = 5. Now if I subtract both x - x this is zero but this is plus. So y + y this is 2 y then 13 - 5 this is 8 then if I divide both side by 2 we find out y = 4 so x= 9 y = 4 but remember that recall x = 3 ^ m / 2 and y = 2 ^ m / 2 I substitute both value here so x is = to x = 3 ^ m / 2. This is 9. It will be 3 ^ 2. And y = 2 ^ m / 2. This is 4. 4. It will be 2 the power 2. Our target m is equal to what? Now this is base is 3. This is 3. So according to exponential formula, you can say here is exponent is equal m / 2 is equal to 2.

[00:05:07]Then if I divide if I multiply both side by two we are find out m= 4. So our final answer m is equal to 4. Here is same case it will be m / 2 is = 2 because of that this value and this value both will same. So this is m is = 2 * 2 this is four. So our final answer is m = 4. So our question which is 3 ^ m - 2 ^ m is equal to 65.

[00:05:40]But you can say this 65 it will be it will be 81 - 16 81 - 16 is equ= to 65.

[00:05:50]Then this is 3 ^ m - 2 ^ m. Then you can see it will be 3 ^ 4 minus 2 ^ 4. Now if I compare both this and this this is three, this is three, this is two and this is two. So this time you can say here m is equal to 4. So you can solve this question like this method. Thank you all. If you enjoy this math problem, please subscribe my channel for others interesting video. Goodbye. Take care everyone.