JAMB 1989 · UME · Q12

What are the values of $y$ which satisfy the equation $9^y - 4(3^y) + 3 = 0$ ?

Worked solution (try it first)

Let $u = 3^y$ .
Then $9^y = (3^2)^y = u^2$ , and the equation is $u^2 - 4u + 3 = 0$ .
Factorise: $(u - 1)(u - 3) = 0$ , so $u = 1$ or $u = 3$ .
$3^y = 1 = 3^0$ gives $y = 0$ , and $3^y = 3 = 3^1$ gives $y = 1$ .
So $y = 0$ and 1, option D.

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