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Reducing Equations to Simpler Form

Solve the fol...

Question

Solve the following equations.
$3^{2 x + 1} = 3^{x + 2} + \sqrt{1 - {6.3}^{x} + 3^{2 (x + 1)}}$

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Solution

$3^{2 x + 1} = 3^{x + 2} + \sqrt{(1)^{2} - {2.1.3}^{x + 1} + (3^{x + 1})^{2}}$
$3^{2 x + 1} = 3^{x + 2} + 3^{x + 1} - 1$
${3.3}^{2 x} = {12.3}^{x} - 1$
$(3^{x})^{2} - {2.2.3}^{x} + 4 = 11 / 3$
$(3^{x} - 2)^{2} = 11 / 3$
$x = l o g_{3} (2 + \sqrt{11 / 3})$

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Reducing Equations to Simpler Form

Standard VIII Mathematics

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