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# log3 x + 11 log3 x3 = 14

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log3 x + 11 log3 x3 = 14

Jan 24, 2015

#1
+99377
+5

do you mean

$$\\log_3 x + 11 log_3 x^3 = 14\\\\ log_3 x + 33 log_3 x = 14\\\\ 34 log_3 x = 14\\\\ log_3 x = \frac{14}{34}\\\\ \frac{logx}{log3} = \frac{14}{34}\\\\ logx = \frac{14}{34}\times log3\\\\ 10^{logx} =10^{\left( \frac{14}{34}\times log3\right)}\\\\ x =10^{\left( \frac{7}{17}\times log3\right)}\\\\$$

$${{\mathtt{10}}}^{\left({\frac{{\mathtt{7}}}{{\mathtt{17}}}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{3}}\right)\right)} = {\mathtt{1.572\: \!033\: \!125\: \!399\: \!619\: \!1}}$$

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Jan 25, 2015

#1
+99377
+5

do you mean

$$\\log_3 x + 11 log_3 x^3 = 14\\\\ log_3 x + 33 log_3 x = 14\\\\ 34 log_3 x = 14\\\\ log_3 x = \frac{14}{34}\\\\ \frac{logx}{log3} = \frac{14}{34}\\\\ logx = \frac{14}{34}\times log3\\\\ 10^{logx} =10^{\left( \frac{14}{34}\times log3\right)}\\\\ x =10^{\left( \frac{7}{17}\times log3\right)}\\\\$$

$${{\mathtt{10}}}^{\left({\frac{{\mathtt{7}}}{{\mathtt{17}}}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{3}}\right)\right)} = {\mathtt{1.572\: \!033\: \!125\: \!399\: \!619\: \!1}}$$

Melody Jan 25, 2015