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$${\frac{{{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)}}{{{log}}_{{\mathtt{2}}}{\left({\mathtt{4\,096}}\right)}}} = -{\mathtt{4}}$$

 Mar 14, 2015

Best Answer 

 #1
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$${\frac{{{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)}}{{{log}}_{{\mathtt{2}}}{\left({\mathtt{4\,096}}\right)}}} = -{\mathtt{4}}$$

 

$${{log}}_{{\mathtt{2}}}{\left({\mathtt{4\,096}}\right)} = {\mathtt{12}}$$

 

$${\frac{{{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)}}{{\mathtt{12}}}} = -{\mathtt{4}}$$

 

$${{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)} = -{\mathtt{48}}$$

 

$${{\mathtt{x}}}^{-{\mathtt{48}}} = {\frac{{\mathtt{37}}}{{\mathtt{999}}}}$$

 

$${\frac{{\mathtt{1}}}{{{\mathtt{x}}}^{{\mathtt{48}}}}} = {\frac{{\mathtt{37}}}{{\mathtt{999}}}}$$

 

$${\mathtt{999}} = {\mathtt{37}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{48}}}$$

 

$${\mathtt{27}} = {{\mathtt{x}}}^{{\mathtt{48}}}$$

 

$${\sqrt[{{\mathtt{{\mathtt{48}}}}}]{{\mathtt{27}}}} = {\mathtt{x}}$$

 

$${\sqrt[{{\mathtt{{\mathtt{48}}}}}]{{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}}} = {\mathtt{x}}$$

 

$${\mathtt{x}} = {\sqrt[{{\mathtt{{\mathtt{16}}}}}]{{\mathtt{3}}}}$$

.
 Mar 14, 2015
 #1
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+10
Best Answer

$${\frac{{{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)}}{{{log}}_{{\mathtt{2}}}{\left({\mathtt{4\,096}}\right)}}} = -{\mathtt{4}}$$

 

$${{log}}_{{\mathtt{2}}}{\left({\mathtt{4\,096}}\right)} = {\mathtt{12}}$$

 

$${\frac{{{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)}}{{\mathtt{12}}}} = -{\mathtt{4}}$$

 

$${{log}}_{{\mathtt{x}}}{\left({\frac{{\mathtt{37}}}{{\mathtt{999}}}}\right)} = -{\mathtt{48}}$$

 

$${{\mathtt{x}}}^{-{\mathtt{48}}} = {\frac{{\mathtt{37}}}{{\mathtt{999}}}}$$

 

$${\frac{{\mathtt{1}}}{{{\mathtt{x}}}^{{\mathtt{48}}}}} = {\frac{{\mathtt{37}}}{{\mathtt{999}}}}$$

 

$${\mathtt{999}} = {\mathtt{37}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{48}}}$$

 

$${\mathtt{27}} = {{\mathtt{x}}}^{{\mathtt{48}}}$$

 

$${\sqrt[{{\mathtt{{\mathtt{48}}}}}]{{\mathtt{27}}}} = {\mathtt{x}}$$

 

$${\sqrt[{{\mathtt{{\mathtt{48}}}}}]{{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}}} = {\mathtt{x}}$$

 

$${\mathtt{x}} = {\sqrt[{{\mathtt{{\mathtt{16}}}}}]{{\mathtt{3}}}}$$

Guest Mar 14, 2015
 #2
avatar+94976 
0

Excellent answer anon :)

 Mar 14, 2015

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