Answer:
The value of y is 81.
Step-by-step explanation:
See the steps below :
[tex] \sqrt{y} - \sqrt[4]{y} - 6 = 0[/tex]
[tex] {y}^{ \frac{1}{2} } - {y}^{ \frac{1}{4} } - 6 = 0[/tex]
[tex]let \: {y}^{ \frac{1}{4} } = x[/tex]
[tex] {x}^{2} - x - 6 = 0[/tex]
[tex](x + 2)(x - 3) = 0[/tex]
[tex]x = - 2[/tex]
[tex] {y}^{ \frac{1}{4} } = - 2[/tex]
[tex] log( {y}^{ \frac{1}{4} } ) = log( - 2) \: (rejected)[/tex]
[tex]x = 3[/tex]
[tex] {y}^{ \frac{1}{4} } = 3[/tex]
[tex] log( {y}^{ \frac{1}{4} } ) = log(3) [/tex]
[tex] \frac{1}{4} log(y) = log(3) [/tex]
[tex] log(y) = 4 log(3) [/tex]
[tex] log(y) = log( {3}^{4} ) [/tex]
[tex] log(y) = log(81) [/tex]
[tex]y = 81[/tex]
