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Solve the fol...

Question

Solve the following equations.
$\sqrt[4]{64} - \sqrt{2^{3 x + 3}} + 12 = 0$

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Solution

$\sqrt{8} - 2^{3 x / 2} . \sqrt{8} + 12 = 0$
$\frac{\sqrt{8} + 12}{\sqrt{8}} = 2^{3 x / 2}$
$1 + 3 \sqrt{2} = 2^{3 x / 2}$
S.B.S,
$(1 + 3 \sqrt{2})^{2} = (2^{3 x / 2})^{2}$
$1 + 18 + 6 \sqrt{2} = 2^{3 x}$
$19 + 6 \sqrt{2} = 2^{3 x}$
Anti log,
$l o g_{2} (19 + 6 \sqrt{2}) = l o g_{2} 2^{3 x}$
$3 x = l o g_{2} (19 + 6 \sqrt{2})$
$x = \frac{l o g_{2} (19 + 6 \sqrt{2})}{3}$

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