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

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

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Answer 1 · 2016-12-07T03:32:28

Let $t = 5^{x}$ $t = 5^x$ .

$t^{2} + 3 t = 28$ $t^2 + 3t = 28$

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

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

$t = - 7 and 4$ $t= -7 and 4$

Now, since $t = 5^{x}$ $t= 5^x$ :

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

$ln (5^{x}) = ln (- 7) and ln (5^{x}) = ln 4$ $ln(5^x) = ln(-7) and ln(5^x) = ln4$

$x = \emptyset and x ln 5 = ln 4$ $x = O/ and xln5 = ln4$

$x = \frac{ln 4}{ln 5}$ $x = ln4/ln5$

Hopefully this helps!

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