Germany | Can you solve? | A nice math olympiad algebra problems |

Ajouté : 2026-05-05

[00:00:01]Hello everyone. Welcome to Rasa's Classroom. Today we are solving an interesting exponential viral math olympiad question.

[00:00:09]Which is 5 to the power x * 25 ^ x is equal to 30. X is equal to what? So how to solve this interesting math problem?

[00:00:19]So our math solution.

[00:00:25]Our question which is 5 to the power x times 25 power is x is equal to 30. This is our question.

[00:00:37]Now this is 5 to the power x.

[00:00:40]But this 25 you can say that it will be 5 to the power 2 bracket whole to the power x is equal to 30.

[00:00:52]Then at this moment I want to apply this math formula here. A to the power n bracket whole to the power m which is a to the power nm.

[00:01:04]If I apply this math formula here so this is 5 to the power x times 5 to the power 2 * x it will be 2x is equal to 30.

[00:01:19]Then this is 5 this is 5 both base are same. So we know that a to the power n times a to the power m which is a to the power n + m.

[00:01:34]If I apply this math formula here so this expression it will be 5 to the power x + 2x x is equal to 30.

[00:01:46]Then this is 5 to the power x + 2x which is 3x is equal to 30.

[00:01:55]Now at this moment I use both side natural log.

[00:01:59]So log 5 to the power 3x is equal to log 30. I use both side natural log.

[00:02:12]Then this exponent move on in front according to exponential formula. We know that log a to the power r which is r log a.

[00:02:23]If I apply this math formula here so this 3x move on in front so it will be 3x times log 5 is equal to log 30.

[00:02:38]Now at this moment I divide both side by log 5.

[00:02:43]So which is 3x times log 5 divide log 5 is equal to log 30 divide log 5. I solved this interesting math problem step by step.

[00:03:05]Now this this cancel. We are find out 3x is equal to log 30 over log 5.

[00:03:17]Now you can say this expression it will be 3x is equal to log 30. It will be log 5 times 6. 5 * 6 this is 30 and this is log 5.

[00:03:33]Now we know that log ab which is log a + log b.

[00:03:43]If I apply this math formula here so this expression which is 3x is equal to log 5 + log 6 over log 5.

[00:03:59]Now I separate this fraction.

[00:04:01]Uh if I separate this fraction we are find out 3x is equal to log 5 over log 5 then which is log 6 over log 5.

[00:04:16]Now this this cancel it will be 1.

[00:04:19]We are find out it will be 3x is equal to 1 + log 6 over log 5.

[00:04:28]This is our final answer. And again if I evaluate this log 6 we are find out which is [snorts] 3 3x is equal to 1 + log 6. It will be log 2 * 3. 2 * 3 this is 6 and here is log 5.

[00:04:51]I solved this interesting math problem step by step.

[00:04:55]And this is 3x is equal to 1 + this is log 2. I apply this math formula again here log 3 over log 5.

[00:05:08]Then this is 3x is equal to 1 + and if I separate this fraction we are find out log 2 over log 5 + log 3 over log 5.

[00:05:26]Now here is 3x is equal to 1 + and if I apply here is natural log formula it will be log 2 base 5 + this is log 3 base 5.

[00:05:42]Now at this moment if I divide both side by 3 so it will be 3x over 3 and this is 1 over 3 + this is log 2 base 5 over 3 + this is log 3 base 5 over 3. I divide both side by 3.

[00:06:03]Now 3 3 cancel. This is x is equal to 1 over 3 + this is [clears throat] 1 over 3 log 2 base 5 + this is 1 over 3 log 3 base 5.

[00:06:20]This is our final answer in this interesting math olympiad question.

[00:06:28]Let's check out or let's verify.

[00:06:32]Our question which is 5 to the power x times 25 bracket power is x is equal to 30.

[00:06:42]This is our question. Now uh if I evaluate this expression we are find out this is 5 to the power 3x is equal to 30.

[00:06:55]Now this is 5 and this is 3 but remember that this x uh if I take this 3 here least common below and this is 1 + log 2 base 5 + this is log 3 base 5 is equal to 30.

[00:07:19]Now at this moment you can say this 3 this 3 cancel.

[00:07:24]We are find out this is 5 to the power 1 + log 2 base 5 then this is + log 3 base 5 is equal to 30.

[00:07:40]Now this is 5 to the power 1 times this is 5 to the power log 2 base 5 times this is 5 to the power log 3 base 5 is equal to 30.

[00:07:56]Now you can say this is 5 times and if I apply here is natural log formula this 5 and this same so it will be 2 times this 5 and this 5 same this is 3 is equal to 30.

[00:08:14]Now this is 10 2 * 5 10 10 * 3 this is 30 is equal to 30. So left hand side and right hand side both side is equal.

[00:08:24]Thank you all if you enjoy this math problem please subscribe my channel for other interesting video. Goodbye. Take care everyone.