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

Question

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

anonymous · Answer

$$3^{2x}-2*3^{x+5} + 3^{10} = 0$$

Is it right?

anonymous · Answer

yes, hope so

anonymous · Answer

yeh thats how its written

anonymous · Answer

x=5

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

ok thank you

anonymous · Answer

i think i need help with the steps?

anonymous · Answer

please?

anonymous · Answer

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?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

oh i get it thank you