How do you solve $2(5^(6x))-9(5^(4x))+13(5^(2x))-6 = 0$ ?

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Answer 1 · 2015-08-14T09:59:50

$x = 0 " or " x = 1/2log_5 2" or " x = 1/2log_5 (3/2)$

$2(5^(6x))-9(5^(4x))+13(5^(2x))-6 = 0$

Take $y = 5^(2x)$

$2y^3-9y^2+13y-6 = 0$
$(y-1)(y-2)(2y-3) = 0$

$5^(2x) = 1 " or " 5^(2x) = 2" or " 5^(2x) = 3/2$
$x = 0 " or " x = 1/2log_5 2" or " x = 1/2log_5 (3/2)$

How do you solve 2(5^(6x))-9(5^(4x))+13(5^(2x))-6 = 02(5^(6x))-9(5^(4x))+13(5^(2x))-6 = 0?