# explaination required

• Mar 7th 2010, 04:56 AM
decoy808
explaination required
Use the substitution $y=3^x$to solve the equation $3^{2x}-10 . 3^x+9=0$

the problem i need explaining is the first part involving the subsitution for $y^2$. how does $3^{2x}$ become $y^2$

$y^2-10y+9=0$

$(y-1)(y-9)=0$
.....

i can see how the rest of the problem is solved as i have the solution

many thanks
• Mar 7th 2010, 05:30 AM
Prove It
Quote:

Originally Posted by decoy808
Use the substitution $y=3^x$to solve the equation $3^{2x}-10 . 3^x+9=0$

the problem i need explaining is the first part involving the subsitution for $y^2$. how does $3^{2x}$ become $y^2$

$y^2-10y+9=0$

$(y-1)(y-9)=0$
.....

i can see how the rest of the problem is solved as i have the solution

many thanks

Because $3^{2x} = \left(3^x\right)^2 = y^2$.