Предмет: Математика,
автор: badurov
Помогите пожалуйста
Приложения:
Ответы
Автор ответа:
0
1.
ОДЗ:
![x-8 textgreater 0\
x textgreater 8](https://tex.z-dn.net/?f=x-8+textgreater++0%5C%0Ax+textgreater++8%0A "x-8 textgreater 0\
x textgreater 8")
2.
![16^{x} =256\
2^{4x}=2^8\
4x=8\x=2](https://tex.z-dn.net/?f=16%5E%7Bx%7D+%3D256%5C%0A2%5E%7B4x%7D%3D2%5E8%5C%0A4x%3D8%5Cx%3D2 "16^{x} =256\
2^{4x}=2^8\
4x=8\x=2")
3.
![( frac{1}{19} )^{x-7}= frac{1}{361} \
( frac{1}{19} )^{x-7}= (frac{1}{19})^2 \
x-7=2\
x=8](https://tex.z-dn.net/?f=%28+frac%7B1%7D%7B19%7D+%29%5E%7Bx-7%7D%3D+frac%7B1%7D%7B361%7D+%5C%0A%28+frac%7B1%7D%7B19%7D+%29%5E%7Bx-7%7D%3D+%28frac%7B1%7D%7B19%7D%29%5E2+%5C%0Ax-7%3D2%5C%0Ax%3D8%0A%0A%0A "( frac{1}{19} )^{x-7}= frac{1}{361} \
( frac{1}{19} )^{x-7}= (frac{1}{19})^2 \
x-7=2\
x=8")
4.
![22^{2x+38}=1\
22^{2x+38}=22^0\
2x+38=0\
2x=-38\
x=-19](https://tex.z-dn.net/?f=22%5E%7B2x%2B38%7D%3D1%5C%0A22%5E%7B2x%2B38%7D%3D22%5E0%5C%0A2x%2B38%3D0%5C%0A2x%3D-38%5C%0Ax%3D-19 "22^{2x+38}=1\
22^{2x+38}=22^0\
2x+38=0\
2x=-38\
x=-19")
5.
ОДЗ:
![x+41 textgreater 0\x textgreater -41\
log_{7}(x+41)=4\
log_{7}(x+41)=4log_{7}7\
log_{7}(x+41)=log_{7}7^4\
x+41=2401\x=2360](https://tex.z-dn.net/?f=x%2B41+textgreater++0%5Cx+textgreater++-41%5C%0Alog_%7B7%7D%28x%2B41%29%3D4%5C%0Alog_%7B7%7D%28x%2B41%29%3D4log_%7B7%7D7%5C%0Alog_%7B7%7D%28x%2B41%29%3Dlog_%7B7%7D7%5E4%5C%0Ax%2B41%3D2401%5Cx%3D2360%0A%0A%0A "x+41 textgreater 0\x textgreater -41\
log_{7}(x+41)=4\
log_{7}(x+41)=4log_{7}7\
log_{7}(x+41)=log_{7}7^4\
x+41=2401\x=2360")
6.
ОДЗ:
![3x-9 textgreater 0\3x textgreater 9\x textgreater 3\
log_{ frac{1}{5} }(3x-9)=-4\
log_{ frac{1}{5} }(3x-9)=-4log_{ frac{1}{5} }{ frac{1}{5} }\
log_{ frac{1}{5} }(3x-9)=log_{ frac{1}{5} }(frac{1}{5})^{-4}\
3x-9=625\
3x=634\
x= frac{634}{3}](https://tex.z-dn.net/?f=3x-9+textgreater++0%5C3x+textgreater++9%5Cx+textgreater++3%5C%0Alog_%7B+frac%7B1%7D%7B5%7D+%7D%283x-9%29%3D-4%5C%0Alog_%7B+frac%7B1%7D%7B5%7D+%7D%283x-9%29%3D-4log_%7B+frac%7B1%7D%7B5%7D+%7D%7B+frac%7B1%7D%7B5%7D+%7D%5C%0Alog_%7B+frac%7B1%7D%7B5%7D+%7D%283x-9%29%3Dlog_%7B+frac%7B1%7D%7B5%7D+%7D%28frac%7B1%7D%7B5%7D%29%5E%7B-4%7D%5C%0A3x-9%3D625%5C%0A3x%3D634%5C%0Ax%3D+frac%7B634%7D%7B3%7D+ "3x-9 textgreater 0\3x textgreater 9\x textgreater 3\
log_{ frac{1}{5} }(3x-9)=-4\
log_{ frac{1}{5} }(3x-9)=-4log_{ frac{1}{5} }{ frac{1}{5} }\
log_{ frac{1}{5} }(3x-9)=log_{ frac{1}{5} }(frac{1}{5})^{-4}\
3x-9=625\
3x=634\
x= frac{634}{3}")
7.
![sin^2x-5sinx-6=0\
sinx=t, t in [-1;1]\
t^2 -5t-6=0\
D=25+24=49\
t_1= frac{5+7}{2}=6 notin [-1;1]\
t_2=-1\
sinx=-1\
x=- frac{ pi }{2} +2 pi k, k in Z](https://tex.z-dn.net/?f=sin%5E2x-5sinx-6%3D0%5C%0Asinx%3Dt%2C+t+in+%5B-1%3B1%5D%5C%0At%5E2+-5t-6%3D0%5C%0AD%3D25%2B24%3D49%5C%0At_1%3D+frac%7B5%2B7%7D%7B2%7D%3D6+notin++%5B-1%3B1%5D%5C%0At_2%3D-1%5C%0Asinx%3D-1%5C%0Ax%3D-+frac%7B+pi+%7D%7B2%7D+%2B2+pi+k%2C+k+in+Z%0A "sin^2x-5sinx-6=0\
sinx=t, t in [-1;1]\
t^2 -5t-6=0\
D=25+24=49\
t_1= frac{5+7}{2}=6 notin [-1;1]\
t_2=-1\
sinx=-1\
x=- frac{ pi }{2} +2 pi k, k in Z")
========================================
1.
![9^{x+3} leq 729\
9^{x+3} leq 9^3 \
x+3 leq 3\
x leq 0](https://tex.z-dn.net/?f=9%5E%7Bx%2B3%7D+leq+729%5C%0A9%5E%7Bx%2B3%7D+leq+9%5E3+%5C%0Ax%2B3+leq+3%5C%0Ax+leq+0 "9^{x+3} leq 729\
9^{x+3} leq 9^3 \
x+3 leq 3\
x leq 0")
2.
![( frac{1}{13} )^{x+7} textless frac{1}{169} \
( frac{1}{13} )^{x+7} textless (frac{1}{13})^2 \
x+7 textgreater 2\
x textgreater -5](https://tex.z-dn.net/?f=%28+frac%7B1%7D%7B13%7D+%29%5E%7Bx%2B7%7D+textless+++frac%7B1%7D%7B169%7D+%5C%0A%28+frac%7B1%7D%7B13%7D+%29%5E%7Bx%2B7%7D+textless+++%28frac%7B1%7D%7B13%7D%29%5E2+%5C%0Ax%2B7+textgreater++2%5C%0Ax+textgreater++-5 "( frac{1}{13} )^{x+7} textless frac{1}{169} \
( frac{1}{13} )^{x+7} textless (frac{1}{13})^2 \
x+7 textgreater 2\
x textgreater -5")
3.
ОДЗ:
![x+17 textgreater 0\x textgreater -17\
log_8(x+17) textless 3\
log_8(x+17) textless 3log_88\
log_8(x+17) textless log_88^3\
x+17 textless 512\ x textless 495](https://tex.z-dn.net/?f=x%2B17+textgreater++0%5Cx+textgreater++-17%5C%0Alog_8%28x%2B17%29+textless++3%5C%0Alog_8%28x%2B17%29+textless++3log_88%5C%0Alog_8%28x%2B17%29+textless++log_88%5E3%5C%0Ax%2B17+textless++512%5C+x+textless++495 "x+17 textgreater 0\x textgreater -17\
log_8(x+17) textless 3\
log_8(x+17) textless 3log_88\
log_8(x+17) textless log_88^3\
x+17 textless 512\ x textless 495")
ответ:
4.
ОДЗ:
![x textgreater 0\
log_{0.9}x geq 2\
log_{0.9}x geq 2log_{0.9}0.9\
log_{0.9}x geq log_{0.9}0.9^2\
x leq 0.81](https://tex.z-dn.net/?f=x+textgreater++0%5C%0Alog_%7B0.9%7Dx+geq+2%5C%0Alog_%7B0.9%7Dx+geq+2log_%7B0.9%7D0.9%5C%0Alog_%7B0.9%7Dx+geq+log_%7B0.9%7D0.9%5E2%5C%0Ax+leq+0.81%0A "x textgreater 0\
log_{0.9}x geq 2\
log_{0.9}x geq 2log_{0.9}0.9\
log_{0.9}x geq log_{0.9}0.9^2\
x leq 0.81")
ответ:
ОДЗ:
2.
3.
4.
5.
ОДЗ:
6.
ОДЗ:
7.
========================================
1.
2.
3.
ОДЗ:
ответ:
4.
ОДЗ:
ответ:
Интересные вопросы
Предмет: История,
автор: realgirl14
Предмет: Математика,
автор: prytkovadara5
Предмет: Геометрия,
автор: horosilovaana65
Предмет: Математика,
автор: francuz565