Đáp án: $P=482$

Giải thích các bước giải:

$\log x(yz)=4\to \log_xyz+1=5\to \log_xxyz=5\to \log_{xyz}x=\dfrac15$

$\log_yzx=5\to \log_yzx+1=6\to \log_yxyz=6\to \log_{xyz}y=\dfrac16$

$\to \log_{xyz}x+\log_{xyz}y=\dfrac15+\dfrac16$

$\to \log_{xyz}xy=\dfrac{11}{30}$

$\to \log_{xy}xyz=\dfrac{30}{11}$

$\to \log_{xy}z+1=\dfrac{30}{11}$

$\to \log_{xy}z= \dfrac{19}{11}$

$\to \log_zxy=\dfrac{11}{19}$

$\to a=11, b=19$

$\to P=11^2+19^2=482$