समाधान 3log(sqrt{2}+1)=log_{2}(x-1)^2

$$3 \log ( \sqrt { 2 } + 1 ) = \log _ { 2 } ( x - 1 ) ^ { 2 }$$

x को लागि हल गर्नुहोस् (complex solution)

$$x=1+\left(-1\right)\times 2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}\text{, }n_{1}\in \mathrm{Z}\text{, }\left(\left(\left(-1\right)Im(\ln(\left(1+\left(-1\right)\times 2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}-1\right)^{2}))+\left(-1\right)\ln(5)\ln(2)^{-1}Im(\ln(\left(1+\left(-1\right)\times 2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}-1\right)^{2}))=0\text{ and }not(1+\left(-1\right)\times 2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}=1)\right)\text{ and }not(1+\left(-1\right)\times 2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}=1)\right)\text{ and }not(1+\left(-1\right)\times 2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}=1)$$

$$x=1+2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}\text{, }n_{1}\in \mathrm{Z}\text{, }\left(\left(\left(-1\right)Im(\ln(\left(1+2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}-1\right)^{2}))+\left(-1\right)\ln(5)\ln(2)^{-1}Im(\ln(\left(1+2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}-1\right)^{2}))=0\text{ and }not(1+2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}=1)\right)\text{ and }not(1+2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}=1)\right)\text{ and }not(1+2^{\frac{1}{2}\left(\ln(5\times 2^{\frac{1}{2}}+7)+\left(-2i\right)\pi n_{1}\right)\log(e)}=1)$$

x को लागि हल गर्नुहोस्

$$x=-\left(5\sqrt{2}+7\right)^{\frac{\log(2)}{2}}+1\approx -0.488814001$$

$$x=\left(5\sqrt{2}+7\right)^{\frac{\log(2)}{2}}+1\approx 2.488814001$$