A certain brand of calculator computes the logarithm $\log _ { a } b$ by pressing $\log$（1）$a$（ $b$ ）. A student computing $\log _ { a } b$ (where $a > 1$ and $b > 1$ ) pressed the buttons in the wrong order, pressing $\log$（1）$b$（ $a$ ） instead, obtaining a result that is $\frac { 9 } { 4 }$ times the correct value. Select the relationship between $a$ and $b$.\\
(1) $a ^ { 2 } = b ^ { 3 }$\\
(2) $a ^ { 3 } = b ^ { 2 }$\\
(3) $a ^ { 4 } = b ^ { 9 }$\\
(4) $2 a = 3 b$\\
(5) $3 a = 2 b$