Question

Решить уравнение $(log_{x}(2))(log_{x/16}(2))=log_{x/64}(2)$

Answer 1

$(log_{x}2)(log_{ frac{x}{16}}2)=log_{ frac{x}{64} }2 \ x>0;x neq 1;x neq 16;x neq 64 \ cfrac{1}{log_{2}x} cdot cfrac{1}{log_{2} frac{x}{16}} =cfrac{1}{log_{2} frac{x}{64}} \ frac{1}{log_{2}x} cdot frac{1}{log_{2}-log_{2}16} =frac{1}{log_{2}-log_{2}64} \ frac{1}{log_{2}x} cdot frac{1}{log_{2}-4} =frac{1}{log_{2}-6}$
$log_{2}x=a \ frac{1}{a} cdot frac{1}{a-4} =frac{1}{a-6} \ frac{1}{a(a-4)} =frac{1}{a-6} \ a(a-4)=a-6 \ a^2-4a-a+6=0 \ a^2-5a+6=0 \ (a-2)(a-3)=0 \ a_1=2 \ log_{2}x_1=2 \ x_1=2^2=4 \ a_2=3 \ log_{2}x_2=3 \ x_2=2^3=8$
Ответ: 4; 8

Answer 2

спасибо