u^v-5v+10=5 ਨੂੰ ਹੱਲ ਕਰੋ

$${ u }^{ v } -5v+10=5$$

u ਲਈ ਹਲ ਕਰੋ (ਜਟਿਲ ਹੱਲ)

$$u=e^{\frac{Im(v)arg(-5\left(1-v\right))+iRe(v)arg(-5\left(1-v\right))}{\left(Re(v)\right)^{2}+\left(Im(v)\right)^{2}}-\frac{2iRe(v)\pi n_{1}}{\left(Re(v)\right)^{2}+\left(Im(v)\right)^{2}}-\frac{2\pi n_{1}Im(v)}{\left(Re(v)\right)^{2}+\left(Im(v)\right)^{2}}}\left(|5\left(1-v\right)|\right)^{\frac{Re(v)-iIm(v)}{\left(Re(v)\right)^{2}+\left(Im(v)\right)^{2}}}$$

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

u ਲਈ ਹਲ ਕਰੋ

$$\left\{\begin{matrix}u=\left(5\left(v-1\right)\right)^{\frac{1}{v}}\text{, }&\left(v\leq 1\text{ and }Numerator(v)\text{bmod}2=1\text{ and }Denominator(v)\text{bmod}2=1\right)\text{ or }\left(\left(5v-5\right)^{\frac{1}{v}}<0\text{ and }v>1\text{ and }Denominator(v)\text{bmod}2=1\right)\text{ or }\left(\left(5v-5\right)^{\frac{1}{v}}>0\text{ and }v>1\right)\\u=-\left(5\left(v-1\right)\right)^{\frac{1}{v}}\text{, }&\left(Numerator(v)\text{bmod}2=1\text{ and }Numerator(v)\text{bmod}2=0\text{ and }Denominator(v)\text{bmod}2=1\text{ and }v<1\right)\text{ or }\left(v>1\text{ and }\left(5v-5\right)^{\frac{1}{v}}>0\text{ and }Numerator(v)\text{bmod}2=0\text{ and }Denominator(v)\text{bmod}2=1\right)\text{ or }\left(v>1\text{ and }\left(5v-5\right)^{\frac{1}{v}}<0\text{ and }Numerator(v)\text{bmod}2=0\right)\end{matrix}\right.$$