Question

(5/6)^4x=(36/25)^9-x, please help solve for x, and the 9-x is all superscript

Answer 1

(25/36)^2x=(36/25)^9-x
(36/25)^-2x=(36/25)^9-x

-2x=9-x
-x=9
x=-9

Answer 2

`(36)/(25)=(6^2)/(5^2)=\left((6)/(5)\right)^2=\left((5)/(6)\right)^(-2)\\\\therefore:\\\\\left((5)/(6)\right)^(4x)=\left[\left((5)/(6)\right)^(-2)\right]^(9-x)\\\\\left((5)/(6)\right)^(4x)=\left((5)/(6)\right)^(-2(9-x))\iff4x=-2(9-x)\\\\4x=-2\cdot9-2\cdot(-x)\\\\4x=-18+2x\ \ \ \ \ |subtract\ 2x\ from\ both\ sides\\\\2x=-18\ \ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{x=-9}`



`Use:\\a^(-n)=\left((1)/(a)\right)^n\\\\\left(a^n\right)^m=a^(n\cdot m)\\\\\left((a)/(b) \right)^n=(a^n)/(b^n)`