 Hello folks, welcome once again to problem solving and in this session we have taken a different equation, this is not an algebraic equation, we have taken an exponential equation. Now what is an exponential equation you know, let's understand that first and then we'll see how we can use the methods known for quadratic equations to solve exponential equations. For that matter any expression, exponential expression will be of the form of a to the power x right, so a to the power x is nothing but where a is a constant, a is constant and x is variable okay, so this is how is it different from algebraic expression, so if you see algebraic expression will be of the order of the nature x to the power a, where x is variable a is constant here, it's upside down, so the base and the exponent has, have changed their places right, so hence bases are constant but the exponents are variables and if you have an expression containing those terms then it is called an exponential expression and when you equate this exponential expression to anything else it becomes an exponential equations, so if you see here 2 is the base, x minus 2 is there is a variable power on 2, similarly 3 minus x is a variable, x is a variable so hence 3 minus x keeps on changing so hence 3 minus x itself is variable varying and hence the base is 2, so base is constant power is variable so hence you know and there are 2 such terms and then they are added together and equated to 3, so hence this is an equation, exponential equation, how to solve them, very good, let's try and solve them, so hence can we simplify this a little bit, so if you see using the exponential rules we can say to the power x minus 2 is to the power x divided by 2 to the power 2, similarly you can see 2 to the power 3 by 2 to the power x is equal to 3, this is what we can say by a to the power minus n is equal to 1 upon a to the power n, this we have learned in the rules of indices, so now what, so if you simplify further it is 2 to the power x to the power upon 4 plus 8 upon 2 to the power x is equal to 3, now we will play our card, definitely this is not a quadratic but let us say y is equal to 2 to the power x, I can say that, so the equation is reduced to y upon 4 plus 8 upon y is equal to 3, so this implies it is y square plus 32 having the common denominator as 4y, correct, is equal to 32, is equal to 3 sorry, so hence if you reduce it further it is y square plus 32 is equal to 12y and this will become y square minus 12y plus 32 equal to 0, so hence y square minus 4y minus 8y splitting the middle term 32 equal to 0, so this implies y times y minus 4 minus 8 times y minus 4 is equal to 0, isn't it, so this implies y minus 4 times y minus 8 is equal to 0, right, so hence y is either 4 or y is either 8 but we want x not y, so what was x, so if you see y is equal to 2 to the power x, let us write it again, so 2 to the power x is equal to 4, so can be written as 2 square and here similarly 2 to the power x can be written as 2 to the power 3, so if the bases are same then in an equation, exponential equation we can equate the coefficient, sorry the exponent, so hence x is 2 and here x equals 3, right, so for exponential equation what you need to do, you make sure the bases are same, the bases are same then you can equate the exponent, so hence there are 2 values, 2 roots to this equation x equals to 2 and x equals 3 my friend, so hence even exponential equations can be reduced to quadratic equation and then can be solved.