The half-life $T$ of a radioactive substance is defined as ``every time period $T$ passes, the mass of the substance decays to half of its original amount''. A lead container contains two radioactive substances $A$ and $B$ with half-lives $T _ { A }$ and $T _ { B }$ respectively. At the start of recording, the masses of these two substances are equal. After 112 days, measurement shows that the mass of substance $B$ is one-quarter of the mass of substance $A$. Based on the above, which of the following is the relationship between $T _ { A }$ and $T _ { B }$? (1) $- 2 + \frac { 112 } { T _ { A } } = \frac { 112 } { T _ { B } }$ (2) $2 + \frac { 112 } { T _ { A } } = \frac { 112 } { T _ { B } }$ (3) $- 2 + \log _ { 2 } \frac { 112 } { T _ { A } } = \log _ { 2 } \frac { 112 } { T _ { B } }$ (4) $2 + \log _ { 2 } \frac { 112 } { T _ { A } } = \log _ { 2 } \frac { 112 } { T _ { B } }$ (5) $2 \log _ { 2 } \frac { 112 } { T _ { A } } = \log _ { 2 } \frac { 112 } { T _ { B } }$
The half-life $T$ of a radioactive substance is defined as ``every time period $T$ passes, the mass of the substance decays to half of its original amount''. A lead container contains two radioactive substances $A$ and $B$ with half-lives $T _ { A }$ and $T _ { B }$ respectively. At the start of recording, the masses of these two substances are equal. After 112 days, measurement shows that the mass of substance $B$ is one-quarter of the mass of substance $A$. Based on the above, which of the following is the relationship between $T _ { A }$ and $T _ { B }$?\\
(1) $- 2 + \frac { 112 } { T _ { A } } = \frac { 112 } { T _ { B } }$\\
(2) $2 + \frac { 112 } { T _ { A } } = \frac { 112 } { T _ { B } }$\\
(3) $- 2 + \log _ { 2 } \frac { 112 } { T _ { A } } = \log _ { 2 } \frac { 112 } { T _ { B } }$\\
(4) $2 + \log _ { 2 } \frac { 112 } { T _ { A } } = \log _ { 2 } \frac { 112 } { T _ { B } }$\\
(5) $2 \log _ { 2 } \frac { 112 } { T _ { A } } = \log _ { 2 } \frac { 112 } { T _ { B } }$