Mister Exam
9^(-x)+8*3^(-x)<0 inequation
The solution
Detail solution
Given the inequality:
$$9^{- x} + 8 \cdot 3^{- x} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$9^{- x} + 8 \cdot 3^{- x} = 0$$
Solve:
$$x_{1} = \frac{- \log{\left(8 \right)} + i \pi}{\log{\left(3 \right)}}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$9^{- 0} + 8 \cdot 3^{- 0} < 0$$
but
so the inequality has no solutions
$$9^{- x} + 8 \cdot 3^{- x} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$9^{- x} + 8 \cdot 3^{- x} = 0$$
Solve:
$$x_{1} = \frac{- \log{\left(8 \right)} + i \pi}{\log{\left(3 \right)}}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0
$$9^{- 0} + 8 \cdot 3^{- 0} < 0$$
9 < 0
but
9 > 0
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
This inequality has no solutions