Помогите 20 Балов!!!!!!. Created by Infalible. algebra-ru

Помогите 20 Балов!!!!!!...

spasibo3pajbrh

task/29887931

ответ : 1. → 16 ; 2 .→ 7 ; 3 . → 0. 1 ; √10

1 votes Thanks 1

oganesbagoyan 4 - ая строка ?

oganesbagoyan log₂ (x) =2² ⇒ x =2⁴ =16

oganesbagoyan

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(1)
$log_{16}( log_{2}( log_{ \sqrt[4]{2} }(x) ) ) = 0.5 \\ log_{2}( log_{ \sqrt[4]{2} }(x)) = \sqrt{16} \\ log_{ \sqrt[4]{2} }(x) = {2}^{4} \\ {4} log_{2}(x) = {2}^{4} \\ log_{2}(x) = {2}^{2} \\ x = {2}^{4} \\ x = 16$
(2)

$5 - 2 log_{7}(x) = 3 \sqrt{ log_{7}(x) } \\ y = \sqrt{ log_{7}(x) } > 0\\ 5 - 2{y}^{2} = 3y \\ 2{y}^{2} + 3y - 5 = 0 \\ 2(y - 1)(y + 2.5) = 0 \\ y1 = 1 \\ y2 = - 2.5 \\$

у2 нам не подходит

Возвращаемся к замене

$\sqrt{ log_{7}(x)} = 1 \\ log_{7}(x) = 1 \\ x = 7$
(3)
$log_{10}(10 {x}^{2} ) log_{10}(x) = 1 \\ (log_{10}(10) + 2 log_{10}(x) ) log_{10}(x) = 1 \\ (1 + 2 log_{10}(x) )log_{10}(x) = 1 \\ y = log_{10}(x) \\ (1 + 2y)y = 1 \\ 2 {y}^{2} + y - 1 = 0 \\ 2(y + 1)(y - \frac{1}{2} ) = 0 \\ y_1= - 1 \\ y_2 = \frac{1}{2} \\ \\ log_{10}(x) = - 1 \\ x = {10}^{ - 1} \\ x_1 = 0.1 \\ \\ log_{10}(x) = 0.5 \\ x = {10}^{0.5} \\ x_ 2 = \sqrt{10} \\$

2 votes Thanks 1

oganesbagoyan logₓⁿ b =( logₓ b ) / n иначе (1/n)*(logₓ b) ... = (log₂ x) / (1/4) =4log₂ x

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