This tricky exponential math question confuses many.Can you solve it?

Welcome back to my channel. We are asked to find X. Yes, this is easy but very tricky. So, let's get straight to the point. X is an exponent and the only way to bring it down is using logarithm, all right? I'd like you to watch to the end but I'm going to see the proof that the answer we got is correct and that is the most important aspect of this video, not even to find it but to prove that X we got is correct. So, let's go. Now, the first thing we need to remember is that using this law of logarithm, okay, let's introduce log to both sides. So, we are going to have log 5 to the power of X minus 2 is equal to log 45, okay? Now, recall that log A to the power of B is equal to B multiplied by log A. Therefore, we can write this as this X will come down, X minus 3 comes down. So, we have X minus 2 multiplied by log 5, right, is equal to log 45. Please subscribe to the channel, turn on your notification bell if this is the first time you have seen this wonderful channel. Give us a thumbs up if you love what we are doing, okay? Comment, yeah, very important. Please drop your comments. That tells me what you feel about my videos, how to improve, and where to tell myself. Well done, JJ, you are doing a great job, okay? Alright, so looking at this, we need to divide both sides. So, let's divide both sides by log 5, okay? You know our intention is to get X. So, if we do that, we are going to have X minus 2 multiplied by log 5 divided by log 5 is equal to log 45 divided by log 5. Now, log 5, we take away log 5 here, then we have X minus 2, okay, is equal to log 45 divided by log 5. If we factorize 45, we will have 3 times 3 times 5, right? Because 45 is same as 9 times 5, which is equal to 3 times 3 times 5. Therefore, we are going to write this as X minus 2 is equal to log 3 multiplied by 3 multiplied by 5 divided by log 5. Then we have X minus 2 is equal to log, now 3 times 3 is 3 squared, multiplied by 5 divided by log 5. So, we have X minus 2 is equal to, now let's recall that, recall that log A multiplied by B, okay, is equal to log A plus log B, is equal to log A plus log B. Therefore, we can write this as X minus 2 is equal to log 3 plus log 5 divided by log 5, okay? Have you subscribed yet? If you have not, then please do, okay? If not, this might be the last time you will see my video. So, in order to ensure that my video is sent to you, or the notification is sent to you, okay? Alright, so from here, recall that A plus B divided by C is the same as A divided by C plus B divided by C, alright? Therefore, we can then write this as X minus 2 is equal to log 3, oh 3 squared, sorry, log 3 squared divided by log 5 plus log 5 divided by log 5, okay? Now, I want you to note, recall that log A to the power of B, just like we did during the first time, is the same thing as B multiplied by log A. Therefore, we write this as X minus 2 is equal to, this 2 will come down to become 2 log 3 divided by log 5 plus, now log 5 will go into itself, 1 plus 1, okay? Now, we have negative 2 here, let's add 2 to both sides, okay? Add 2 to both sides. Remember, you need to see how I proved that the answer I got is correct. Like I said, some might be able to get the value of X, but can you prove that the answer is correct? Now, we have add 2 to both sides, so we are going to have plus 2 plus 2, right? So, this minus 2 plus 2 is 0, so we are left with X is equal to 2 log 3 divided by log 5 plus 3, all right? Now, recall that log A divided by log B is equal to log A base B, all right? So, we can now write this as X is equal to 2 log 3 base 5 plus 3, and this is what we have as our X, okay? 2 log 3 base 5 plus 3. Now, to the main thing while we are shooting this video, let us prove that this is actually our answer. Let's do that. Stay tuned, stay tuned. This is where this video gets more interesting. Okay, now we have 5 to the power of, our X is the whole of this 2 log 3 base 5 plus 3, then minus 2, right? Minus 2. Now, is this equal to 45? Is it? So, we have 5 to the power of 2 log 3 base 5. Now, 3 minus 2 is 1 plus 1. Now, is this equal to 45? Next thing we need to do is recall that A to the power of m plus n is equal to A to the power of m multiplied by A to the power of n, all right? Therefore, we can actually rewrite this as 5 to the power of 2 log 3 base 5 multiplied by 5 to the power of 1. Now, is this actually equal to 45? Let's continue. So, let us take this to become power of this, right? Since log A to the power of B is same thing as B log A, okay? So, this one is already in this form. Let us take it back to this form. So, this B will come up to power of A. So, 2 will come up to become power of 3. How are you doing? So, now we have 5 to the power of log 3. Now, raise to the power of this 2 base 5 multiplied by 5 to the power of 1. Now, is this equal to 45? Okay. So, we have 5 to the power of log 9 because 3 to the power of 3 is 9 base 5 multiplied by 5 because 5 to the power of 1 is 5. Now, is this actually equal to 45? Now, recall another logarithmic law. I told you this is going to be interesting. Recall the logarithmic law that says that A raise to the power of log B base A is equal to B. Now, what are we taking from here? You can see that this base A and this base A that they are the same. So, everything here becomes just this B, right? If we apply the same thing here, you are going to see that this and this are the same. Therefore, the whole of this is what? 9 multiplied by 5, right? Now, is this actually 45? Yeah, 9 times 5 is 45. So, we have 45 is equal to 45 and that proves that the answer we got is absolutely correct. Thank you so much for watching and thanks for always supporting me especially if you actually always watch to the end. I am grateful. Thanks for supporting my channel and thank you for everything. See you in my next video and don't forget to comment. Tell me what you actually feel about this video, how I can improve and yeah have a nice day. Bye.