10^n=v^n+2*2*9-ஐ தீர்க்கவும்

$$10 ^ { n } = v ^ { n } + 2 \times 2 \times 9$$

v-க்காகத் தீர்க்கவும் (சிக்கலான தீர்வு)

$$v=\left(|36-10^{n}|\right)^{\frac{Re(n)-iIm(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}}e^{\frac{Im(n)arg(-\left(36-10^{n}\right))+iRe(n)arg(-\left(36-10^{n}\right))}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}-\frac{2i\pi n_{1}Re(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}-\frac{2\pi n_{1}Im(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

v-க்காகத் தீர்க்கவும்

$$\left\{\begin{matrix}v=\left(10^{n}-36\right)^{\frac{1}{n}}\text{, }&\left(n\neq 2\log(6)\text{ and }Numerator(n)\text{bmod}2=1\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(\left(10^{n}-36\right)^{\frac{1}{n}}>0\text{ and }n>2\log(6)\right)\text{ or }\left(\left(10^{n}-36\right)^{\frac{1}{n}}<0\text{ and }Denominator(n)\text{bmod}2=1\text{ and }n>2\log(6)\right)\text{ or }n=2\log(6)\\v=-\left(10^{n}-36\right)^{\frac{1}{n}}\text{, }&\left(n\neq 2\log(6)\text{ and }Numerator(n)\text{bmod}2=1\text{ and }Numerator(n)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(\left(10^{n}-36\right)^{\frac{1}{n}}<0\text{ and }Numerator(n)\text{bmod}2=0\text{ and }n>2\log(6)\right)\text{ or }\left(\left(10^{n}-36\right)^{\frac{1}{n}}>0\text{ and }Numerator(n)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\text{ and }n>2\log(6)\right)\text{ or }\left(n=2\log(6)\text{ and }Numerator(2\log(6))\text{bmod}2=0\right)\end{matrix}\right.$$