Question

solve
9^x-10x3^x+9=0

Answer 1

let y = 3^x , then 9^x = (3^2)^x = (3^x)^2 = y^2,  so we can write the equation as

y^2 - 10y + 9 = 0

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

giving y = 9 or y = 1

Therefore  3^x = 9    giving x = 2

and 3^x = 1 giving x = 0


so the solution  set is {0, 2}

Note - I have assumed that the 'x' after the 10 means 'multiply'.   Is that correct?