Question

Помогите пожалуйста!!!33 балла за один пример!

Answer 1

$log_ab + log^{-1}_ab = 3\\\\log_ab + \frac{1}{log_ab} = 3$

$(log_ab + \frac{1}{log_ab})^2 = 3^2 \\\\log^2_ab+ 2\cdot log_ab\cdot \frac{1}{log_ab} + \frac{1}{log^2_ab} = 9 \\\\log^2_ab+ 2 + \frac{1}{log^2_ab} = 9 \\\\log^2_ab+ \frac{1}{log^2_ab} = 7 \\\\\\log^2_ab+ log^{-2}_ab = 7$

Answer 2

$1)log_{a}b+log_{a}^{-1}=3\\\\(log_{a}b +\frac{1}{log_{a}b })^{2}=3^{2}\\\\ log_{a}^{2}b+2*log_{a}b*\frac{1}{log_{a}b }+(\frac{1}{log_{a}b })^{2}=9\\\\log_{a}^{2}b+2+\frac{1}{log_{a}^{2}b  }=9\\\\log_{a}^{2}b+\frac{1}{log_{a}^{2}b}=7$

$2)log_{a}^{2} b+log_{a}^{-2}b=log_{a}^{2}b+\frac{1}{log_{a}^{2}b}=7$