Question

Решите уравнение:
log4 (1,6 — 6x) = log4 (16x — 0,6) — 1​

Answer 1

$0,175;$

Объяснение:

ОДЗ:

$1,6-6x0;$

$-6x-1,6;$

$x$

$x$

$x$

$16x-0,60;$

$16x0,6;$

$x\frac{0,6}{16};$

$x\frac{3}{80};$

$x\in(\frac{3}{80}; \frac{4}{15});$

$log_{4}(1,6-6x)=log_{4}(16x-0,6)-1;$

$log_{4}(1,6-6x)=log_{4}(16x-0,6)-log_{4}4;$

$log_{4}(1,6-6x)=log_{4}((16x-0,6):4);$

$log_{4}(1,6-6x)=log_{4}(4x-0,15);$

$1,6-6x=4x-0,15;$

$-4x-6x=-1,6-0,15;$

$-10x=-1,75;$

$x=0,175;$

$0,175=\frac{175}{1000};$

$\frac{3}{80}=\frac{3*12,5}{80*12,5}=\frac{37,5}{1000};$

$0,175\frac{3}{80};$

$\frac{4}{15}=\frac{4*200}{15*200}=\frac{800}{3000};$

$\frac{175}{1000}=\frac{175*3}{1000*3}=\frac{525}{3000};$

$0,175$