JAMB 1994 · UME · Q9

Solve for $x$ if $25^x + 3(5^x) = 4$ .

Worked solution (try it first)

Let $u = 5^x$ .
Then $25^x = (5^2)^x = u^2$ , and the equation is $u^2 + 3u - 4 = 0$ .
Factorise: $(u + 4)(u - 1) = 0$ , so $u = 1$ or $u = -4$ .
$5^x$ is never negative, so reject $-4$ .
From $5^x = 1 = 5^0$ , $x = 0$ , option B.

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