Question

please help! i need to solve for x in the problem: 3^(2x)-2*3^(x+5) + 3^10 =0

Answer 1

\[3^{2x}-2*3^{x+5} + 3^{10} = 0\]

Is it right?

Answer 2

yes, hope so

Answer 3

yeh thats how its written

Answer 4

x=5

Answer 5

3^x=t
t^2-2*3^5t+3^10=0

Answer 6

So then do I combine the "-2*3^5t ?"

Answer 7

just complete the square and you'll get (t-3^5)^2=0

Answer 8

ok thank you

Answer 9

i think i need help with the steps?

Answer 10

please?

Answer 11

Like uzma said use a substitution t=3^x. First notice that 3^(x+5)=(3^x)*(3^5)=(3^5)*y. Then the equation reduces to t^2-2(3^5)y+3^10=0. Then solve this as a quadratic in y, using 'complete the square'. Make sense?

Answer 12

I used y so when you see y think of it as t

Answer 13

before i complete the square do i simplify to t^2-6^5t+3^10?

Answer 14

oh i get it thank you