How do you solve $25^ { x } - 8\cdot 5^ { x } = - 16$ ?

Question

1714 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-22T07:00:11

$x=log_5(2)$

$(5^2)^x-8 *5^x=-16$
$t^2-8t=-16$
$t=4$
$5^x=4$

Answer 2 · 2018-06-22T07:01:01

$color(maroon)(x = log 4 / log 5 = 0.8614$

$25^x - 8 * 5^x + 16 = 0$

Let $5^x = a$

$=> a^2 - 8a + 4^2 = 0$

$(a-4)^2 = 0$

$:. a = 4$

$a = 5^x = 4$

$x log 5 = log 4$

$x = log(4) / log(5) = 0.8614$

How do you solve 25^ { x } - 8\cdot 5^ { x } = - 1625^ { x } - 8\cdot 5^ { x } = - 16?