Log_1/7(4x+1)=-2;
log_1/7(4x+1)=log_1/7(49);
4x+1=49;
4x=48;
x=12.
ОДЗ:
4x+1>0;
4x>-1;
x>-1/4.
Ответ: 12.
ЭТО ПРОВЕРЕННЫЙ ОТВЕТ!!!
1) (2⁹
![2^{ \frac{4}{5} }](https://tex.z-dn.net/?f=+2%5E%7B+%5Cfrac%7B4%7D%7B5%7D+%7D+)
*1*
![2^{ \frac{1}{5} }](https://tex.z-dn.net/?f=+2%5E%7B+%5Cfrac%7B1%7D%7B5%7D+%7D+)
*
![2^{-8}](https://tex.z-dn.net/?f=+2%5E%7B-8%7D+)
=
![2^{9+ \frac{4}{5}+ \frac{1}{5}-8 }](https://tex.z-dn.net/?f=+2%5E%7B9%2B+%5Cfrac%7B4%7D%7B5%7D%2B+%5Cfrac%7B1%7D%7B5%7D-8++%7D+)
=2²=4
2)
![3^{x}](https://tex.z-dn.net/?f=+3%5E%7Bx%7D+)
(27+1)=
![2^{x}](https://tex.z-dn.net/?f=+2%5E%7Bx%7D+)
(5-16-17), вынесли общий множитель за скобки
28*
![3^{x}](https://tex.z-dn.net/?f=+3%5E%7Bx%7D+)
=
![2^{x}](https://tex.z-dn.net/?f=+2%5E%7Bx%7D+)
*63, поделим каждую часть на
![2^{x}](https://tex.z-dn.net/?f=+2%5E%7Bx%7D+)
*28≠0
![( \frac{3}{2}) ^{x}](https://tex.z-dn.net/?f=+%28+%5Cfrac%7B3%7D%7B2%7D%29+%5E%7Bx%7D+)
=
![\frac{63}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B63%7D%7B28%7D+)
![( \frac{3}{2}) ^{x}](https://tex.z-dn.net/?f=+%28+%5Cfrac%7B3%7D%7B2%7D%29+%5E%7Bx%7D+)
=
![\frac{9}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B9%7D%7B4%7D+)
x=2
A1=4
an+1=a1+3
a5=?
a5=a1+4d
a5=4+4d
4d=4
d=1
a5=4+4=8
an+1=a1+d
an+1=a1+1