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Given that

 

 

 

 

find n^3.

 Apr 3, 2020
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\(log_{4n}(40\sqrt{3})=log_{3n}(45)\\ find\ n^3\)

 

Hello Guest!

 

\(log_{4n}(40\sqrt{3})=log_{3n}(45)=z\)

 

\((4n)^z=40\sqrt{3}\)  

\( (3n)^z=45\)                         | \(\times\ \frac{(4n)^z}{(3n)^z}=\frac{4^zn^z}{3^zn^z}=(\frac{4}{3})^z\)

\((\frac{4}{3})^z\cdot(3n)^z=45\cdot (\frac{4}{3})^z \)

 

\(z\cdot ln(4n)=ln(40\cdot \sqrt{3})\\ z=ln(40\cdot \sqrt{3})/ln(4n)\\ z\cdot ln(3n)=ln(45\cdot \sqrt{3})\\ z=ln(45\cdot \sqrt{3})/ln(3n)\)      

 

To be continued.

laugh  !

 Apr 3, 2020
edited by asinus  Apr 4, 2020
edited by asinus  Apr 4, 2020

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