Mathematics, 23.09.2019 03:30 Jbutler15
(5/6)^4x=(36/25)^9-x, solve for x, and the 9-x is all superscript
Answers: 2
![\frac{36}{25}=\frac{6^2}{5^2}=\left(\frac{6}{5}\right)^2=\left(\frac{5}{6}\right)^{-2}\\\\therefore:\\\\\left(\frac{5}{6}\right)^{4x}=\left[\left(\frac{5}{6}\right)^{-2}\right]^{9-x}\\\\\left(\frac{5}{6}\right)^{4x}=\left(\frac{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}](/tpl/images/0253/7809/0bfe2.png)
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(5/6)^4x=(36/25)^9-x, solve for x, and the 9-x is all superscript...
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