00:01
This question, we have to solve the following equation.
00:04
It's, if we notice carefully, that's a quadratic in terms of 2 raise to x.
00:08
And how's that? let's try to rewrite 2 raise to 2x as 2 raise 2x whole square.
00:14
Because after all, this means that 2 and x will be multiplied and we get 2x, minus 9 times 2 raise 2x and that is equal to 20.
00:23
Now we're going to substitute 2 raise 2 x as y.
00:27
This would mean that this will become y square minus 9.
00:30
Y is equal to 20 and subtracting 20 both sides this will be y square minus 9 y minus 20 is equal to 0 and clearly this can be factorized as uh 4 and 5 minus 4 so we write minus 4 and interesting no it won't be 4 and 5 that has to be uh 4 times 5 is 20 but that has to be one of it but we are also looking for minus 9 let's see 10 and 2 2 that will also not work.
01:08
You don't think so this can be factorized.
01:11
So let's try to use the quadratic formula, which is minus of minus 9, which is 9 plus minus square root of minus 9 square minus 4 times a is 1 and c is minus 20 over 2 times 1.
01:26
So that is going to be 9 plus minus minus 9 squared is 81.
01:33
That will be 81 plus 80 over 2 over 2 that is the value of y so that's going to be 9 plus minus root of 161 over 2 so the possible values of y which is nothing but 2 raised 2 x is going to be 2 9 plus root of 161 over 2 and another value is 2 raise 2 x is equal to 9 minus root of 161 over 2 now 161 is definitely more than 9 because 9 square is just 81, 161 square is little less than 13.
02:10
If i want to approximate using a calculator, that is somewhere around 12 .69.
02:17
So root 161 is somewhere around 12 .69.
02:20
And clearly 9 minus 12 .69 is negative.
02:23
This means that 2 raise 2x is coming as negative, which is not possible because 2 raise 2x range, range of an exponential function is always positive because 2...