Question

log3 x* log0,2 x=4log0.2 3

Answer 1

$log_3(x) * log_{0,2}(x) = log_{0,2}(3) \ log_{3}(x) * frac{log_3(x)}{log_3(0,2)} = log_{0,2}(3) \ frac{log_3(x) * log_3(x)}{log_3(0,2)} = log_{0,2}(3) \ frac{log_3(x)^2}{log_3(0,2)} = log_{0,2}(3) \ log_3(x)^2 = log_{0,2}(3) * log_3{(0,2)} \ log_3(x)^2 = frac{log_3(3)}{log_3(0,2)} * log_3(0,2) \ log_3(x)^2 = frac{1}{log_3(0,2)} * log_3{0,2} \ log_3(x)^2 = 1 \ log_3(x)^2 =+- sqrt{1} \ log_3(x)=1 \ log_3(x)=-1 \ x_1=3^1=3 \ x_2=3^{-1}= frac{1}{3}$