2-x-2-3x-16-solve-for-x-

Question Number 90762 by Ar Brandon last updated on 25/Apr/20

2^{x} + 2^{3 x} = 16

solve for x

Answered by MJS last updated on 25/Apr/20

2^{x} = t

t^{3} + t - 16 = 0

D = \frac{{(1)}^{3}}{27} + \frac{{(- 16)}^{2}}{4} > 0 \Rightarrow Cardano

t_{1} = \sqrt[3]{8 + \frac{\sqrt{5187}}{9}} - \sqrt[3]{- 8 + \frac{\sqrt{5187}}{9}}

\Rightarrow x = \frac{1}{\ln 2} \ln (\sqrt[3]{8 + \frac{\sqrt{5187}}{9}} - \sqrt[3]{- 8 + \frac{\sqrt{5187}}{9}})

t_{1} \approx 2.38769

x \approx 1.25561

Facebook Tweet Pin