Question

ПОМОГИТЕ РЕШИТЬ 66 НОМЕР!!!

Answer 1

2)преобразуем 1/0,5+log16(2)=1/1/2+1/4=1/3/4=4/3,  8^4/3=(2^3)^4/3=16

logV4 из2 (х-3)=log по осн 2^1/4 (x-3)=4log2(x-3), получаем  16=4log2(x-3),  log2(x-3)=4  ,x-3=2^4,  x=19

Answer 2

1) ОДЗ : x > 0

$log_{6sqrt[6]{6} }x=-frac{12}{7}\\log_{6^{frac{7}{6}}}x=-frac{12}{7}\\x=(6^{frac{7}{6}})^{-frac{12}{7}}=6^{-2}=frac{1}{36}$

2) ОДЗ : x > 3

$2)8^{frac{1}{0,5+log_{16}2}}=log_{sqrt[4]{2}}(x-3)\\8^{frac{1}{0,5+0,25}}=log_{sqrt[4]{2} }(x-3)\\8^{^{frac{4}{3}}}=log_{sqrt[4]{2} }(x-3)\\log_{sqrt[4]{2}}(x-3)=16\\x-3=(sqrt[4]{2})^{16}\\x-3=16\\x=19$

3) ОДЗ : x ≠ 3 ; x ≠ 4 ;

(x - 3)(x - 4) > 0      ⇒   x ∈ (- ∞ ; 3) ∪ (4 ; + ∞)

$frac{1}{3}*(frac{1}{4})^{log_{4}frac{x-3}{x-4}}=frac{log_{4}4 }{x-3}\\frac{1}{3}*frac{x-4}{x-3}=frac{1}{x-3}\\frac{x-4}{3}=1\\x-4=3\\x=7$