9·6^x + 8·18^x >54^x | ·1/6^x
9 + 8·3^x > 9^x
-9^x +8·3^x +9 >0
9^x -8·3^x -9 <0
3^x = y
y² - 8y - 9 < 0 ( y1 = 9 , y2 = -1)
<u>-∞ + -1 - 9 + +∞
</u> IIIIIIIIIIIIIII
-1 < y < 9
-1 < 3^x < 9
3^x < 9
3^x < 3²
x < 2
а-а^3-15а-4/а^2-16=
=а(а^2-16)/а^2-16 - а^3-15а-4/а^2-16=
=(а^3-16а-а^3+15а+4)/а^2-16=
=4-а/а^2-16=4-а/(а-4)(а+4)= а-4/(а-4)(а+4)=-1/а+4
![81^{7}-27^{9}-9^{13}=(3^{4})^{7}-(3^{3})^{9}-(3^{2})^{13}=3^{28}-3^{27}-3^{26}= \\ =3^{26}(3^{2}-3-1)=3^{26}(9-3-1)=3^{26}*5=3^{2}*3^{24}*5=9*5*3^{24} \\ =45*3^{24}](https://tex.z-dn.net/?f=81%5E%7B7%7D-27%5E%7B9%7D-9%5E%7B13%7D%3D%283%5E%7B4%7D%29%5E%7B7%7D-%283%5E%7B3%7D%29%5E%7B9%7D-%283%5E%7B2%7D%29%5E%7B13%7D%3D3%5E%7B28%7D-3%5E%7B27%7D-3%5E%7B26%7D%3D+%5C%5C+%3D3%5E%7B26%7D%283%5E%7B2%7D-3-1%29%3D3%5E%7B26%7D%289-3-1%29%3D3%5E%7B26%7D%2A5%3D3%5E%7B2%7D%2A3%5E%7B24%7D%2A5%3D9%2A5%2A3%5E%7B24%7D+%5C%5C+%3D45%2A3%5E%7B24%7D+)
кратно 45, значит делится нацело на 45.
X^2-16=0
(x-4)(x+4)=0
x-4=0 или x+4=0
x=4 x=-4