Question

If, (3/4)^6 x (16/9)^5 = (4/3)^ x+2, What is the value of x?

Answer 1

x = 2

Explanation:

`\bigg( (3)/(4) \bigg)^(6) *\bigg( (16)/(9) \bigg)^(5) = \bigg( (4)/(3) \bigg)^(x + 2) \\ \\ \bigg( (3)/(4) \bigg)^(6) *\bigg( \frac{ {4}^(2) }{ {3}^(2) } \bigg)^(5) = \bigg( (4)/(3) \bigg)^(x + 2) \\ \\ \frac{ {3}^(6) }{ {4}^(6) } * \frac{ {4}^(10) }{ {3}^(10) } = \bigg( (4)/(3) \bigg)^(x + 2) \\ \\ \frac{ {4}^(10 - 6) }{ {3}^(10 - 6) } = \bigg( (4)/(3) \bigg)^(x + 2) \\ \\ \frac{ {4}^(4) }{ {3}^(4) } = \bigg( (4)/(3) \bigg)^(x + 2) \\ \\ \bigg( (4)/(3) \bigg)^(4) = \bigg( (4)/(3) \bigg)^(x + 2) \\ \\ \implies \: 4 = x + 2 \\ \\ \implies \: x = 4 - 2 \\ \\ \implies \: x = 2`