00:01
Okay, in this question, a equation is given that is 3 raised to the power 2x minus 12 multiplied by 3 raise to the power x plus 27 equals to 0 and we have to solve this equation for x.
00:11
So no problem, 3 raised to the power 2x can be written as 3 raised to the power x whole square, okay? minus 12 .3 raised to the power x plus 27 equals to 0.
00:21
And now we will substitute some t equals to 3 raised to the power x.
00:24
So it will be t square minus 12 t plus 27.
00:28
And now it is a quadratic equation with variable t.
00:31
So we will do the factor of this equation.
00:33
So t square and minus 12t can be written as minus 90 minus 3t plus 27 equals to 0.
00:41
And now from these two we will take t common factor and it will be t minus 9.
00:46
And from these two we will take negative three common factor and it will be t minus 9 equals to 0.
00:52
And we can say t minus 3 and t minus 9 equals to 0...