Here we also have an equation with the logarithm of x So the natural logarithm the logarithm with base e and Here we have the logarithm of x squared is going to be equal to 1 and as always we are looking to isolate X on one side of the equal sign so what we can start with is get rid of that parenthesis here also squared so what we can do then is take the square root on both sides and that We have to be careful with that because on the other side here we get plus or minus the square root of 1 and that is because when we think about a number squared being equal to 1 then we have two choices We have 1 squared It can be equal to 1 but we also have minus 1 squared which can also be equal to 1 so that means that we have both positive and negative versions of the square root of 1 here eh Now the square root of 1 is just equal to 1 so that means that the logarithm of x in that case here is equal to Plus or minus 1 so that means that we have two solutions We have that the logarithm of x can be equal to 1 or we can have the logarithm of x equal to minus 1 So now we've broken it up into two equations eh This is maybe the easiest way to do it but it's actually possible to just use that operator here as it is and you can maybe take that at the end of the video and just take that too but now we have two equations here that we can solve separately and when we have a logarithm with base e then what we like to do here is to put both sides of the equal sign as an exponent to the same base that the logarithm here has which is e so we have e to the ln x is equal to e to the ln before And that's the same thing as saying that Okay if these two numbers are equal then these two numbers will also be equal because I've treated them exactly the same way and now it turns out and so that e to the ln to x is just equal to X so we have X is equal to e to the ln before which is just equal to e so that's a possibility here And on the other side we do exactly the same thing we get e to the power of ln x is equal to e to the power of minus f and then e up ln x It's just X so we get X = e to the minus before which is exactly the same as x Erik 1 over e so Here we have our solutions X is either e or 1 over E now Maybe they should be in ascending order so we can do it this way instead Possibly an alternative way of writing is to just write that x Sorry X is equal to 1 over E or x is equal to e and that's also perfectly fine but back to what we mentioned here that we can actually just use it here as it is and here too we can just take and put eh both sides of both sides of the equal sign as the exponent of e so then we get e to the power of Ln until x is equal to e to the power of Plus minus 1 and then we get X is e to the power of plus minus 1 which again gives two solutions X Wow X is equal to e to the power of POS 1 or x Erik e to the power of neg 1 so that will give exactly the same solution here Can you remove because e up the first is just E and we arrive at exactly same answer and yes just as a little additional note can I mention what the eh notation here means also if you haven't come across it eh here we just write that x is an element of and when we have an element in an interval or a list in that case here we have two individual values that X can be And then we write it in list form and then we use curly brackets like that That means that the numbers We put inside here It's only the numbers that X can be an element of there are also more intervals for example if X can be anything from 1 to 10 then we have used other brackets but in that case here we are going to have it in list form because there are only two individual values that we are looking for here so what it says here is that x is an element in the list 1 over E or e and it just means exactly the same as it says here that Either X is equal to 1 over E Or X is equal to e so it will be exactly the same It's just a question of no rotation