Question

If 9 * 81^x = 1 / 27^x-2, find x

Answer 1

$GOOD \: \: MORNING \: \\ \\ 9 \times (81) {}^{x} = 3 {}^{ - 3(x - 2)} \\ \\ 3 {}^{2} \times 3 {}^{4x} = 3 {}^{ - 3x} \times 3 {}^{6} \\ \\ 3 {}^{4x + 3x} = 3 {}^{6 - 2} \\ \\ 3 {}^{7x} = 3 {}^{4} \\ \\ now \: compare \: powers \: of \: 3 \: \: we \: have \: \\ \\ 7x = 4 \\ \\ x = 4 \div 7$

Answer 2

Step-by-step explanation:

$\begin{lgathered} 9 \times (81) {}^{x} = 3 {}^{ - 3(x - 2)} \\ \\ 3 {}^{2} \times 3 {}^{4x} = 3 {}^{ - 3x} \times 3 {}^{6} \\ \\ 3 {}^{4x + 3x} = 3 {}^{6 - 2} \\ \\ 3 {}^{7x} = 3 {}^{4} \\ \\ Now \: Compare \: Powers \: Of \: 3 \: \: We \: Have \: \\ \\ 7x = 4 \\ \\ x = 4 \div 7\end{lgathered}$