Question

How do I approach the following problem. Please don't give answer but just guidance as to how to approach these in general. I need to be able to solve without a calculator.

3^(2x+1)-16(3^x)+5=0

Answer 1

Distribute

Answer 2

Eventually answered my own question. No idea what distributing has to do with anything though...

I simplified 3^(2x+1) to ((3^x)^2)*3^x then substituted a variable for 3^x and solved the corresponding quadratic. Seems to have worked

Answer 3

I think you were on the right track, except
3^(2x+1) = 3(3^x)(3^x) = 3(3^x)^2

so let y = 3^x to change your equation to
3y^2 - 16y + 5 = 0
(y - 5)(3y - 1) = 0
y = 5 or y = 1/3

so 3^x = 5 or 3^x = 1/3

This cannot be solved WITHOUT a calculator

3^x = 5
log 3^x = log 5
x log3 = log 5
x = log5/log3 = appr. 1.465

but 3^x = 1/3
3^x = 3^-1
x = -1

so x = -1 or x = appr. 1.465

both answers verify in the original