Solve the following equations.
${2.3}^{x + 1} - {6.3}^{x - 1} - 3^{x} = 9$

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Solution

${2.3}^{x + 1} - {6.3}^{x - 1} - 3^{x} = 9$
$3^{x} = t$
$2.3 t - 6 / 3 t - t = 9$
$6 t - 2 t - t = 9$
$3 t = 9$
$t = 2$
$3^{x} = 2$
$x l o g_{3}^{3} = l o g_{3}^{2}$
$x = l o g_{3}^{2}$

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