Solve the following equation...? $2^(4x) - 5(2^(2x - 1/2)) + 2 = 0$

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Answer 1 · 2017-11-26T21:01:12

$x=ln((25+-sqrt(609))/(2sqrt(2)))/(ln4)$

$2^(4x)-5(2^(2x-1/2))+2=0<=>$

$2^((2x)^2)-5*2^(2x)color(red)(xx)5*2^(-1/2)+2=0<=>$

$(2^(2x))^2-(25/sqrt(2))2^(2x)+2=0<=>$

Now the quadratic equation should be easy to see.
You have to replace $2^(2x)$ with an y.

$<=> y^2−(25/(√2))y+2=0$

$y=(25/sqrt(2)+-sqrt(625/2-2*2*2))/2$

$y=(25/sqrt(2)+-sqrt(609/2))/2$

$2^(2x)=y=(25/sqrt(2)+-sqrt(609/2))/2$

Appyling logarithms:

$2xln2=ln((25+-sqrt(609))/(2sqrt(2)))$

$x=ln((25+-sqrt(609))/(2sqrt(2)))/(2ln2)$

$x=ln((25+-sqrt(609))/(2sqrt(2)))/(ln4)$

Solve the following equation...? 2^(4x) - 5(2^(2x - 1/2)) + 2 = 02^(4x) - 5(2^(2x - 1/2)) + 2 = 0