Question

Solve for (9/4) power x+1 ÷ (2/3) power 3x-1 = (3/2) power 11​

Answer 1

$question = (\frac{9}{4})^{x + 1} \div (\frac{2}{3} )^{3x - 1} = (\frac{3}{2}) ^{11} \\ solution. \\ (\frac{ {3}^{2} }{ {2}^{2} })^{x + 1} \times (\frac{3}{2} )^{3x - 1} = (\frac{3}{2}) ^{11} \\ ( \frac{3}{2} ) ^{2(x + 1)} \times (\frac{3}{2} )^{3x - 1} = (\frac{3}{2}) ^{11} \\ ( \frac{3}{2} ) ^{2x + 2} \times (\frac{3}{2} )^{3x - 1} = (\frac{3}{2}) ^{11} \\ formula = {a}^{1} \times {a}^{1} = {a}^{1 + 1} . \\ ( \frac{3}{2} ) ^{(2x + 2 + 3x - 1)} = (\frac{3}{2}) ^{11} \\ (\frac{3}{2}) ^{5x + 1} = (\frac{3}{2}) ^{11} \\ 5x + 1 = 11 \\ 5x = 11 - 1 \\ 5x = 10 \\ x = \frac{10}{5} \\ x = 2 \: \: answer...$