If $5^(2x) + 3(5)^x = 28$ , then what is the value of $x$ ?

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Answer 1 · 2016-12-07T03:32:28

Let $t = 5^x$ .

$t^2 + 3t = 28$

$t^2 + 3t - 28 =0$

$(t + 7)(t - 4) = 0$

$t= -7 and 4$

Now, since $t= 5^x$ :

$5^x = -7 and 5^x = 4$

$ln(5^x) = ln(-7) and ln(5^x) = ln4$

$x = O/ and xln5 = ln4$

$x = ln4/ln5$

Hopefully this helps!

If 5^(2x) + 3(5)^x = 285^(2x) + 3(5)^x = 28, then what is the value of xx?