Решите логарифмические уравнения: 1) Log2 (9-x)=2*log2 (3)2) log7(x+5)=log7(4x-7). Created by az34358strelok8390. algebra-ru

Решите логарифмические уравнения: 1) Log2 (9-x)=2*log2 (3)2) log7(x+5)=log7(4x-7...

az34358strelok8390 @az34358strelok8390

August 2022 2 17 Report

Решите логарифмические уравнения:

1) Log2 (9-x)=2*log2 (3)

2) log7(x+5)=log7(4x-7)

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Verified answer

$1)\; \; log_2(9-x)=2\cdot log_23\; \; ,\quad ODZ:\; 9-x>0\; ,\; \; x$

$2)\; \; log_7(x+5)=log_7(4x-7)\; \; ,\quad ODZ:\; \left \{ {{x+5>0} \atop {4x-7>0}} \right.\; \left \{ {{x>-5} \atop {x>1,75}} \right.\; \; \to \; x>1,75\\\\x+5=4x-7\\\\3x=12\\\\\boxed {x=4}$

3 votes Thanks 1

ElbortGames

$log_{2} (9-x)=2*log_{2} (3)$

$log_{2} (9-x)=log_{2} (3^{2} )$

$9-x=3^{2}$

$x = 0$

Ответ: $x = 0$

$log_{7} (x + 5) = log_{7} (4x - 7)$

$x + 5 = 4x - 7$

$-3x + 5 = -7$

$-3x = -12$

$x = 4$

Ответ: $x = 4$

1 votes Thanks 1

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