Express as a simple logarithm 2ln6 - ln3 .

We start with: 2ln6 - ln3 ... First, we rewrite this expression as: ln6 + ln6 - ln3 ... Next, we rewrite this as: ln(23) + ln(23) - ln3 ... Using the log rule log_axy = log_ax + log_xy, we express this as ln2 + ln3 + ln2 + ln3 - ln3 ... We simplify this to ln2 + ln2 + ln3 ... Using the log rule log_ax + log_ay = log_axy, we express this as ln (223) ... Finally, we can simplify this to ln12. Alternative method: We start with: 2ln6 - ln3 ... First, using the log rule: ylog_ax = log_a(x^y) we express this as ln(6²)- ln3 ... Next, we rewrite this as: ln36 - ln3 ... Using the log rule log_ax - log_xy = log_a(x/y) we express this as ln(36/3) ... Finally, we can simplify this to ln12