Condense the logarithmic expression $\frac{1}{2}\cdot \left(\log_{6}\left(45\right)-\log_{6}\left(5\right)\right)+\log_{6}\left(12\right)$

$\log\left(4\right)64$

$3\ln\left(a\right)-\frac{1}{2}\left(\ln\left(b\right)+\ln\left(c^2\right)\right)$

$2\log_7\left(x\right)$

$\ln\left(x\right)+4\ln\left(y\right)$

$2\ln\left(3x\right)$

$\log\left(\frac{1}{2}\right)\cdot 32$

$\log_3\left(b\right)+\log_3\left(b+2\right)$