Solve the equation $5^{2 x} - 24. 5^{x} - 25 = 0$
find the number of roots .

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Solution

Let $5^{x} = t,$ then the given equation can be reduce in the form.
$t^{2} - 24 t - 254 = 0 \Rightarrow (t - 25) (t + 1) = 0 \Rightarrow t \neq - 1 ∴ t = 25 = 5^{x} ∴ x = 2$
Hence $x = 2$ is only root of the given equation.

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