Question

Log (ab) a=9
Log (ab) b =?
Помогите пожалуйста

Answer 1

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Answer 2

Первый способ:

$\displaystyle log_{ab}a=9;\ log_aba=\frac{1}{9}; log_ab+log_aa=\frac{1}{9};\\log_ab+1=\frac{1}{9};\ log_ab=-\frac{8}{9};\ log_ba=-\frac{9}{8};\\log_ba+1=-\frac{9}{8}+1;\ log_ba+log_bb=-\frac{9}{8}+\frac{8}{8};\\log_bab=-\frac{1}{8};\ \boxed{log_{ab}b=-8;}$

Второй способ:

$log_{ab}ab=1;\ log_{ab}b+log_{ab}a=1;\ log_{ab}b+9=1;\\log_{ab}a=1-9;\ \boxed{log_{ab}a=-8;}$