Question

Solve the equation
9^x+1 - 19 x 3^x + 2 = 0
giving 3 significant figures in your answer where appropriate.

Answer 1

Is it like this
\[\large 9^{x+1}-19x \cdot 3^{x} + 2=0\]

Answer 2

19 multiply 3 power x

Answer 3

Oh...
\[\large \large 9^{x+1}-19 \cdot 3^{x} + 2=0\]
this then?

Answer 4

yea

Answer 5

Okay, @Sgstudent , let's play a game.
First, we let
\[\large u = 3^x\]
So we can write
\[\large \large 9^{x+1}-19 \cdot 3^{x} + 2=9\cdot9^{x}-19\cdot3^{x}+2=9\cdot(3^x)^{2}-19(3^x)+2=9u^2 -19u+2\]
\[\large 9u^2 -19u+2=0\]
Can you do it now?

Answer 6

oh lol i can do it now.

Answer 7

How did you get (3^x)2 ??

Answer 8

Laws of exponents.
\[\huge (a^m)^n = a^{mn}\]

Answer 9

From which a ^mn

Answer 10

Okay, step by step, then :D
\[\large 9^x = (3^2)^x = 3^{2x}=3^{x\cdot2}=(3^x)^2\]

Answer 11

That's what i'm looking for thank you !

Answer 12

No sweat :)

Answer 13

where are you from?