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log3 x + 11 log3 x3 = 14

Guest Jan 24, 2015

Best Answer 

 #1
avatar+94090 
+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
 #1
avatar+94090 
+5
Best Answer

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

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