Question

Solve x = 81^-2 / 729^1-x = (9)^2x​

Answer 1

Step-by-step explanation:

$\frac{ {81}^{ - 2} }{ {729}^{1 - x} } = (9)^{2x} \\ \\ \therefore \: \frac{ {9}^{ - 4} }{ {9}^{3(1 - x)} } = (9)^{2x} \\ \\ \therefore \:\frac{ {9}^{ - 4} }{ {9}^{(3- 3x)} } = (9)^{2x} \\ \\\therefore \: {9}^{ - 4 - (3 - 3x)} = (9)^{2x} \\ \\ \therefore \: {9}^{3x - 7} = (9)^{2x} \\ \\ \implies \: 3x - 7 = 2x \\ \\ \implies \: 3x - 2x = 7\\ \\ \implies \huge \purple{\boxed{ x = 7}}$