How do you solve $5^{x^{2}} = \frac{25}{5^{x}}$ $5^(x^2) = 25/(5^x)$ ?

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Answer 1 · 2017-02-03T14:18:35

${- 2, 1}$ ${-2, 1}$

Cross multiply:

$5^{x^{2}} \cdot 5^{x} = 25$ $5^(x^2) * 5^x = 25$

Simplify using $a^{n} \cdot a^{m} = a^{n + m}$ $a^n * a^m = a^(n + m)$

$5^{x^{2} + x} = 25$ $5^(x^2 + x) = 25$

Write in equivalent bases.

$5^{x^{2} + x} = 5^{2}$ $5^(x^2 + x) = 5^2$

$x^{2} + x = 2$ $x^2 + x =2$

$x^{2} + x - 2 = 0$ $x^2 + x - 2 =0$

$(x + 2) (x - 1) = 0$ $(x + 2)(x- 1) = 0$

$x = - 2 and 1$ $x= -2 and 1$

Hopefully this helps!

How do you solve 5x2=255x5^(x^2) = 25/(5^x)?