Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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

Sagot :

[tex]\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}[/tex]


[tex]Use:\\a^{-n}=\left(\frac{1}{a}\right)^n\\\\\left(a^n\right)^m=a^{n\cdot m}\\\\\left(\frac{a}{b} \right)^n=\frac{a^n}{b^n}[/tex]
ollieboyne
(25/36)^2x=(36/25)^9-x
(36/25)^-2x=(36/25)^9-x

-2x=9-x
-x=9
x=-9
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.