Question

4(3n-2)^(-3/2)+1=347/343

Answer 1

Greetings and Happy Holidays!

Solve for n.

`4(3n-2)^{(-3)/(2)}+1= (347)/(343)`

Add -1 to both sides.

`(4(3n-2)^{(-3)/(2)}+1)+(-1)=((347)/(343))+(-1)`


`4(3n-2)^{(-3)/(2)}=(347)/(343)-1`


`4(3n-2)^{(-3)/(2)}=(347)/(343)-(343)/(343)`


`4(3n-2)^{(-3)/(2)}=(4)/(343)`

Divide both sides by 4

`\frac{4(3n-2)^{(-3)/(2)}}{4}=((4)/(343))/(4)`


`\frac{4(3n-2)^{(-3)/(2)}}{4}=(4)/(343)((1)/(4))`


`\frac{4(3n-2)^{(-3)/(2)}}{4}=(4)/(1372)`


`\frac{4(3n-2)^{(-3)/(2)}}{4}=(1)/(343)`


`(3n-2)^{(-3)/(2)}=(1)/(343)`

Solve the Exponent.

`((3n-2)^{(-3)/(2)})^{(2)/(-3)} =(1)/(343)^{(2)/(-3)}`


`3n-2=49`

Add 2 to both sides.

`(3n-2)+2=(49)+2`


`3n=51`

Divide both sides by 3.

`(3n)/(3)= (51)/(3)`


`n=17`

The Answer Is:

`\left[\begin{array}{ccc}n=17\end{array}\right]`

Hope this helped!
-Benjamin