How do you solve $25^x = 5^(x^2 - 15)$ ?

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Answer 1 · 2016-03-28T11:55:02

$x={-3,5}$

$25^x=5^(x^2-15)$

$color(red)(5)^(2x)=color(red)(5)^(x^2-15)$
$"equation has the same base value"$

$2x=x^2-15$

$x^2-2x-15=0$

$(x-5)(x+3)=0$
$if (x-5)=0" then " x=5$
$if(x+3)=0" then "x=-3$
$x={-3,5}$

How do you solve 25^x = 5^(x^2 - 15)25^x = 5^(x^2 - 15)?