3 ^ { x ^ { 2 } - 3 x } = 81 é
Solve for é
é=\frac{3^{x\left(x-3\right)}}{81}
Solve for x
x=\frac{\sqrt{4\log_{3}\left(é\right)+25}+3}{2}
x=\frac{-\sqrt{4\log_{3}\left(é\right)+25}+3}{2}\text{, }é\geq \frac{3^{\frac{3}{4}}}{2187}
Graph
Share
Copied to clipboard
81é=3^{x^{2}-3x}
Swap sides so that all variable terms are on the left hand side.
\frac{81é}{81}=\frac{3^{x\left(x-3\right)}}{81}
Divide both sides by 81.
é=\frac{3^{x\left(x-3\right)}}{81}
Dividing by 81 undoes the multiplication by 81.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}