Solve the logarithmic equation $\log \left(x-2\right)+\log \left(x-3\right)=\log \left(6\right)$

$2log\left(x\right)-log\left(x+6\right)=0$

$\log_3\left(x+4\right)+\log_3\left(x-4\right)=2$

$\log_2\left(x-2\right)+\log_2\left(x+1\right)=2$

$2\cdot log\left(x\right)-1\cdot log\left(x+6\right)=0$

$\log\left(x-1\right)+\log\left(x+1\right)=2\log\left(x+2\right)$

$\log_5\left(m-8\right)=\log_5\left(2m-15\right)$

$\ln\left(\sqrt{x}\right)=-211111$