Question

упростить логарифмы. даю много

Answer 1

1)

$\displaystyle \sqrt[4]{\frac{a^{log_ab+3}*b^{log_ba+3}}{a^{log_ab-1}*b^{log_ba-1}}}= \sqrt[4]{\frac{a^{log_ab}*a^3*b^{log_ba}*b^3}{a^{log_ab}/a * b^{log_ba}/b}}=\\\\= \sqrt[4]{\frac{b*a^3*a*b^3}{\frac{b*a}{a*b}}}= \sqrt[4]{a^4*b^4}=a*b$

2)

$\displaystyle ((log^2_ab-log^2_ac)-(log_ab+log_ac))*\frac{1}{log_ab/c}=\\\\=((log_ab-log_ac)(log_ab+log_ac)-log_abc)* \frac{1}{log_ab/c}=\\\\= \frac{log_ab/c*log_abc-log_abc}{log_ab/c}= \frac{log_abc(log_ab/c-1)}{log_ab/c}$

можно и дальше преобразовать

$\displaystyle =log_abc-\frac{log_abc}{log_ab/c}=log_abc-log_abc*log_{b/c}a=log_abc(1-log_{b/c}a)$