If log27-x - 2 2-3- find x-

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Conversion of Numbers Using Logarithms

If log27 x = ...

Question

If $l o g_{27} x = 2 \frac{2}{3}$ , find $x$ .

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Solution

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x - \frac{1}{x} = 3 + 2 \sqrt{2}

x^{3} - \frac{1}{x^{3}}

x = 3 + 2 \sqrt{2}

\sqrt{x} - \frac{1}{\sqrt{x}}

x = (2 + \sqrt{3})

{(x^{2} + \frac{1}{x^{2}})}^{2}

x

0

{({log}_{27} x^{3})}^{2} = {log}_{27} x^{6}

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