USA | Brain Booster Math Olympiad Problems | Can you solve it?

Added: 2026-05-05

[00:00:01]Hello everyone. Welcome to my YouTube channel. Welcome to Rasha's Classroom.

[00:00:06]Today we are solving an interesting exponential math problem. Which is 4 to the power x plus 4 to the power x is equal to 40. x is equal to what? Let me explain our solution.

[00:00:21]Our question which is 4 to the power x plus 4 to the power x is equal to 40. This is our question.

[00:00:33]Now, at this moment you can say this is 4 to the power x is common. So if I take 4 to the power x is common so this divide this, this is 1 plus this divide this, this is 1 is equal to 40.

[00:00:49]Then at this moment you can say this is 4 to the power x and 1 plus 1, this is 2 is equal to 40.

[00:01:00]Now, at this moment I divide both side by 2.

[00:01:04]We are find out 4 to the power x times 2 divide 2 is equal to 40 divide 2.

[00:01:15]Then this two this two cancel.

[00:01:18]We are find out a nice exponential equation. 4 to the power x is equal to 40 divide 2. This is 20.

[00:01:26]Then here is x is equal to what? So how to simplify this exponential expression?

[00:01:32]But at this moment I use both set natural log.

[00:01:35]So log 4 to the power x is equal to log 20.

[00:01:42]But we know that log a to the power r which is log a to the power r is equal to r log a.

[00:01:56]If I apply this math formula here, so this exponent x move on in front. So which is x log 4 is equal to log 20.

[00:02:09]Then this is log 4. This is log 20. [snorts] So I divide both side by log 4.

[00:02:17]So which is x log 4 divide log 4 is equal to log 20 divide log 4.

[00:02:31]Now this log 4 this log 4 is cancel out.

[00:02:34]We are find out x is equal to log 20 over log 4.

[00:02:43]Then this log 20 it will be log 4 * 5. 4 * 5 this is 20 and this is log 4.

[00:02:54]>> [clears throat] >> Now at this moment I apply this math formula here.

[00:02:59]Which is log log a b it will be log a plus log b. I apply this math formula here.

[00:03:12]So this expression it will be log 4 plus log 5.

[00:03:21]Then which is log 4.

[00:03:23]Then if I separate this case we are find out it will be log 4 divide this log 4. I separate this fraction.

[00:03:36]And this is log 5 divide log 4.

[00:03:42]Then this 4 this 4 is cancel it will be 1.

[00:03:45]So we are find out which is 1 plus log 5 base 4. This is our final answer. In this exponential math problem or you can say that it 4 it will be 2 to the power 2. So it will be 1 over 2 log 5 base 2.

[00:04:03]So this is our final answer in this exponential math problem.

[00:04:07]Let's verify our question which is 4 to the power x plus 4 to the power x which is 40.

[00:04:17]This is our question.

[00:04:18]But remember that x which is 1 plus log 5 base 4 plus 4 to the power 1 plus log 5 base 4 which is 40. Is it right?

[00:04:33]Let's check out. At this moment if I apply this math formula here a to the power n plus m which is a to the power n times a to the power m so this expression it will be 4 to the power 1 times 4 to the power log 5 base 4 plus this is also 4 to the power 1 times 4 to the power log 5 base 4 is equal to 40.

[00:05:01]Now this is 4 times this is 5 because of that this this same this is 5 plus this is 4 times this is 5 which is 20 plus 20 it will be 40. So left hand side and right hand side both side is equal. So this is our final answer which is x is equal to 1 plus log 5 base 4. Thank you all if you enjoy this math problem please subscribe my channel for other interesting video. Goodbye. Take care everyone.