Tricky exponential math problem that confuses many.

Is it possible that when you raise negative 3 to a power of x you are going to get 3? Is that possible? Yes it is. Welcome back to my channel. So today we are asked to find x if minus 3 to the power of x is equal to 3. All right so first recall that minus 3 can be written as minus 1 multiplied by 3. All right so we are going to replace this with minus 1 multiplied by 3 raised to the power of x is equal to 3. All right now remember that anytime we find square root of negative 1 we always say that this is equal to i right square root of negative 1 is equal to i. Now if I square both I'm going to have square root of negative 1 all squared is equal to i squared and if this removes this we have negative 1 is equal to i squared. So with that I'm going to write out these two equations here that square root of negative 1 is equal to i and negative 1 is equal to i squared. Okay please if this is the first time you are tuning into this channel please subscribe to the channel turn on your notification bell yes so that anytime I upload a new video you will be the first to be notified. All right I would not like to miss you in my next video so please subscribe and always comment. I'm always in the comment section reading your suggestions and everything. Okay so this is where we are now I'm going to substitute this negative 1 with i squared and if I do that I will have 3 i squared right 3 i squared raised to the power of x is equal to 3. Now at this point once the power is what we are looking for we don't have any other option than to introduce log to both sides in order to find x. So if we introduce log introduce log on both sides we are going to have log 3 i squared raised to the power of x is equal to log 3. Okay log 3 i squared to the power of x is equal to Now recall that log a raised to the power of b is equal to b multiplied by log a. Okay so in this case that means this x will come down to multiply log 3 i squared. So we are going to have x log 3 i squared okay is equal to log 3. Now remember that log a b is the same thing as log a plus log b. Moving forward we are going to have x this is going to be log 3 plus log i squared is equal to log 3. Okay now we are going to have x log 3 plus these two will come down to come to log i is equal to log 3. Now remember we are looking for x so we are going to divide both sides of this equation by log 3 plus 2 log i. So we divide this by log 3 plus 2 log i and also divide this side by log 3 plus 2 log i. Therefore this we take away this and we are left with x is equal to this. Okay I don't have any space to write it here. So our x is equal to log 3 divided by log 3 plus 2 log i. Now the second method okay the second method is let us for this method recall that e raised to the power of i multiplied by pi plus 1 is equal to 0 according to urea right. Now we are going to bring out negative 1 from this yes so doing that we are going to have that if we take away 1 from both sides we may have that e to the power of i multiplied by pi is equal to negative 1. Therefore we can now replace this because this minus 3 is negative 1 multiplied by 3 we can write this equation as negative 1 multiplied by 3 raised to the power of x is equal to 3. So I'm going to replace this negative 1 with e to the power of i multiplied by pi. So I will have e to the power of i multiplied by pi multiplied by 3 raised to the power of x is equal to 3. Now I'm going to introduce a line to both sides in order to bring down x. Okay so I will have line e to the power of i pi multiplied by 3 raised to the power of x is equal to length 3. So now if we bring this down using the same law that we used we are going to have x ln e to the power of i pi multiplied by 3 is equal to ln 3. Okay now recall that we can write this as x ln e to the power of i multiplied by pi plus ln 3 right is equal to ln 3. Now we need to bring down i multiplied by pi to this place so we have x i multiplied by pi. I'm not repeating the laws because I've already introduced it in log. Okay that log a raised to the power of b is equal to b multiplied by log a. That is exactly why I'm bringing this down. Okay so now we have i multiplied by pi ln e plus ln 3 is equal to ln 3. Then moving forward we are almost there almost there. So we have to remember that recall that ln e is 1 right. ln e is equal to 1. So we are going to have x into i multiplied by pi plus ln 3 is equal to ln 3. Now let's divide both sides by i pi plus ln 3. Okay so we divide by i multiplied by pi plus ln 3 and divide this side by the same thing. So let's divide this side by the same i multiplied by pi plus ln 3. Now this is going to remove this and we have x is equal to ln 3 divided by i multiplied by pi plus ln 3 and that is the value of x. Thank you so much for watching. See you in my next video. Bye