Solve for C (complex solution)
C=-\left(1-P\right)^{N}+1
Solve for N (complex solution)
\left\{\begin{matrix}N=\frac{2i\pi n_{1}}{\ln(1-P)}+\log_{1-P}\left(1-C\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&C\neq 1\text{ and }P\neq 0\text{ and }P\neq 1\\N\in \mathrm{C}\text{, }&\left(P=1\text{ and }C=1\right)\text{ or }\left(P=0\text{ and }C=0\right)\end{matrix}\right.
Solve for C
C=-\left(1-P\right)^{N}+1
\left(P>1\text{ and }Denominator(N)\text{bmod}2=1\right)\text{ or }\left(P=1\text{ and }N>0\right)\text{ or }P<1
Solve for N
\left\{\begin{matrix}N=\log_{1-P}\left(1-C\right)\text{, }&C<1\text{ and }P\neq 0\text{ and }P<1\\N\in \mathrm{R}\text{, }&\left(P=0\text{ and }C=0\right)\text{ or }\left(P=2\text{ and }C=2\text{ and }Denominator(N)\text{bmod}2=1\text{ and }Numerator(N)\text{bmod}2=1\right)\\N>0\text{, }&P=1\text{ and }C=1\end{matrix}\right.
Share
Copied to clipboard
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}