In the early stages of an infectious disease outbreak, since most people have not been infected and have no antibodies, the total number of infected people usually grows exponentially. Under the premise that ``the initial number of infected people is $P _ { 0 }$ , and each infected person on average infects $r$ uninfected people per day'', the total number of people infected with the disease after $n$ days, $P _ { n }$ , can be expressed as
$$P _ { n } = P _ { 0 } ( 1 + r ) ^ { n } \text {, where } P _ { 0 } \geq 1 \text { and } r > 0 \text { . }$$
Answer the following questions:
(1) Given that $A = \frac { \log P _ { 5 } - \log P _ { 2 } } { 3 } , B = \frac { \log P _ { 8 } - \log P _ { 6 } } { 2 }$ , show that $A = B$ . (4 points)
(2) Given that a certain infectious disease in its early stages follows the above mathematical model and the total number of infected people increases tenfold every 16 days, find the value of $\frac { P _ { 20 } } { P _ { 17 } } \times \frac { P _ { 8 } } { P _ { 6 } } \times \frac { P _ { 5 } } { P _ { 2 } }$ . (5 points)
(3) Based on (2), find the value of $\frac { \log P _ { 20 } - \log P _ { 17 } } { 3 }$ . (4 points)