For a two-digit natural number $N$, when the mantissa of $\log N$ is $\alpha$, $$\frac { 1 } { 2 } + \log N = \alpha + \log _ { 4 } \frac { N } { 8 }$$ Find the value of $N$ that satisfies this equation. [4 points]
For a two-digit natural number $N$, when the mantissa of $\log N$ is $\alpha$,
$$\frac { 1 } { 2 } + \log N = \alpha + \log _ { 4 } \frac { N } { 8 }$$
Find the value of $N$ that satisfies this equation. [4 points]