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arlik [135]
4 years ago
14

216 = (1/36 )^ x−1 how would you solve this?

Mathematics
2 answers:
coldgirl [10]4 years ago
5 0
216= (\frac{1}{36} )^{x-1} \\ 216=(36^{-1})^{x-1} \\ 216=36^{1-x} \\ 216=36^1*36^{-x} \\ 36^{-x}=216:36 \\ 36^{-x}=6 \\( 6^2)^{-x}=6 \\ 6^{-2x}=6^1 \\ -2x=1 \\ x=- \frac{1}{2}
jek_recluse [69]4 years ago
4 0
\hbox{convert the numbers to the powers of 6:} \\ 216 = 6^3 \\
\frac{1}{36}=\frac{1}{6^2}=6^{-2} \\ \\
216=(\frac{1}{36})^{x-1} \\
6^3=(6^{-2})^{x-1} \\
6^3=6^{-2(x-1)} \\
3=-2(x-1) \\
3=-2x+2 \\
3-2=-2x \\
1=-2x \\
x=-\frac{1}{2}
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