Question

9^(x^2) 3^7 x = 81

solve for x

Answer 1

\[\large 9^{x^2}+3^{7x}=81\] Is that what you mean?

Answer 2

yes

Answer 3

yeah

Answer 4

Recognize that 9, and 81 are all multiples of 3 and you can simply factor that 3 out. Do you understand?

Answer 5

kind of what would we do

Answer 6

x^2 + 7 x = 9?

Answer 7

Close. Shouls be 2x^2 + 7x = 4

Answer 8

then solve for x?

Answer 9

wats next

Answer 10

Yes sir solve for x. its a quadratic equation now, so it should be easy

Answer 11

how do you get rid of the 2^(x^2) tho?

Answer 12

Multiply through the equation by 1/2

Answer 13

So that your equation looks like x^2 + 7x/2 - 2 = 0

Answer 14

@incomplte it's to the power of....\(\large 9^{x^2}\)

Answer 15

So? @PhoenixFire

Answer 16

\[\large 9^{x^2}+3^{7x}=81\]Dividing through by 3 would give\[\large 3^{x^2}+1^{7x}=27\] I don't really see how that's helped. How do you get the 'x' out of the power to solve it?

Answer 17

We are combining powers, not dividing by 3

Answer 18

Remember your basic exponential rules?!

Answer 19

How are you combining powers if the base isn't the same? I'm actually curious as to how this is solved.... My brain doesn't agree :(

Answer 20

The bases are the same lol

Answer 21

3^(2x^2)+3^(7x)=3^4

Answer 22

Oh wow.... then \[\large 3^{2x^2+7x}=3^4\]Then take the log to drop the quadratic and the 4 down, the log(3) will cancel on both sides, then you simply solve \[2x^2+7x=4\]

Answer 23

Thanks @incomplte
Sorry for the moment of stupidity :P

Answer 24

No problems