Greetings and Happy Holidays!
Solve for n.
[tex]4(3n-2)^{\frac{-3}{2}}+1= \frac{347}{343}[/tex]
Add -1 to both sides.
[tex](4(3n-2)^{\frac{-3}{2}}+1)+(-1)=(\frac{347}{343})+(-1)[/tex]
[tex]4(3n-2)^{\frac{-3}{2}}=\frac{347}{343}-1[/tex]
[tex]4(3n-2)^{\frac{-3}{2}}=\frac{347}{343}-\frac{343}{343}[/tex]
[tex]4(3n-2)^{\frac{-3}{2}}=\frac{4}{343}[/tex]
Divide both sides by 4
[tex]\frac{4(3n-2)^{\frac{-3}{2}}}{4}=\frac{\frac{4}{343}}{4} [/tex]
[tex]\frac{4(3n-2)^{\frac{-3}{2}}}{4}=\frac{4}{343}(\frac{1}{4})[/tex]
[tex]\frac{4(3n-2)^{\frac{-3}{2}}}{4}=\frac{4}{1372}[/tex]
[tex]\frac{4(3n-2)^{\frac{-3}{2}}}{4}=\frac{1}{343}[/tex]
[tex](3n-2)^{\frac{-3}{2}}=\frac{1}{343}[/tex]
Solve the Exponent.
[tex]((3n-2)^{\frac{-3}{2}})^{\frac{2}{-3}} =\frac{1}{343}^{\frac{2}{-3}} [/tex]
[tex]3n-2=49[/tex]
Add 2 to both sides.
[tex](3n-2)+2=(49)+2[/tex]
[tex]3n=51[/tex]
Divide both sides by 3.
[tex] \frac{3n}{3}= \frac{51}{3}[/tex]
[tex]n=17[/tex]
The Answer Is:
[tex] \left[\begin{array}{ccc}n=17\end{array}\right] [/tex]
Hope this helped!
-Benjamin
