in this video I'm gonna go over this discriminant question disguised as a log question from the IB math SLE exam so at first glance it looks like you're gonna need log properties and log equation skills but you read later in the question it has this language exactly one solution and that's one of our tip offs that this is discriminant question so if you ever see the language about two solutions or one solution exactly one solution that kind of thing you're gonna think discriminant if it's two solutions the discriminant is greater than zero if it's two imaginary solutions to imaginary or no real solutions some language like that we're having a discriminant that is less than zero and if it's exactly one solution which sometimes is written as two repeated because it would be the same value twice which is actually just one value that would be where the discriminant equals zero so here we have exactly one solution the discriminant is gonna equal zero but we have some work to do before we can even see a discriminant in this question but that's what you should be thinking when you see that language so now we can go back up to the top where it says consider f of X equals and we have a log with a base K we're told X has to be between 0 and 2 all right and K is greater than 0 so the base of the log is is greater than 0 the equation f of x equals 2 has exactly one solution so even just writing that the function equals 2 might earn you a point function equals 2 so you always should write whatever you do know just from reading the question we do know that eventually we're gonna be setting our discriminant equal to 0 that also might be worth the point so you should write down anything you do know and now we're looking to our log equation and this is the only step at which I require some log knowledge which is to say if I'm trying to solve a log equation I would want to rearrange it to exponential form so the base of this log is a K so base K and the log equals an exponent so this thing is the exponent in a log equation so I put that on the base so base K to the exponent of 2 would equal the argument of your log so it's just rearranging a log equation to an exponential equation and now I know I'm supposed to have a discriminant set equal to zero and I'm gonna have to rearrange this thing too in order to figure out what my discriminant is gonna be so I'm gonna get everything on one side of the equation 3x squared minus 6x plus K squared equals 0 I'm gonna identify what a B and C are because I know that my discriminant is b squared minus 4ac if I don't know it I can find that in the formula booklet so I'm going to set well actually let's identify this is a it's the 3 and this is B again the C is K squared so it's a little bit of work for us there so we'll say B squared - oops 4 then times a times C equals 0 so I've got everything filled in I have only one variable that's the K so I should be able to solve this equation and this is a non calculator question so if it's a quadratic with this one is it should be factorable or you can use square roots to solve so we're going to divide both sides by 12 3 equals a squared ok equals at first you might be thinking plus or minus three but then we're gonna have to go look up at the top where we see that K is greater than zero so K equals the square root of three that's it