Question

1/2(a power X - a power -X) =1/4(a power X+ a power -X) find X, A value please answer

Answer 1

Step-by-step explanation:

$hello \\ \frac{1}{2} ( {a}^{x} - \frac{1}{ {a}^{x} } ) = \frac{1}{4} ( {a}^{x} + \frac{1}{ {a}^{x} } ) \\ \frac{{a}^{2x } - 1 }{ {a}^{x} } = \frac{1}{2} \frac{ {a}^{2x} + 1 }{ {a}^{x} } \\ 2 {a}^{2x} - 2 = {a}^{2x} + 1 \\ {a}^{2x} = 3 \\ {a}^{x} = \sqrt{3} \\ {a}^{x} = ({3})^{ \frac{1}{2} } \\ \\ a = 3 \: \: \: and \: \: \: x = \frac{1}{2} \\ \\ hope \: the \: solution \: is \: clear \: dear...$

Answer 2

Step-by-step explanation:

$\frac{1}{2} ( {a}^{x} - \frac{1}{ {a}^{x} } ) = \frac{1}{4} ( {a}^{x} + \frac{1}{ {a}^{x} } ) \\ 2 {a}^{x} - \frac{2}{ {a}^{x} } = {a}^{x} + \frac{1}{{a}^{x}} \\ 2 {a}^{2x} - 2 = {a}^{2x} + 1 \\ {a}^{2x} = 3 \\ {a}^{x} = ({3)}^{ \frac{1}{2} } \\ a = 3 \\ x = \frac{1}{2}$