ln (e^6)+log _(2)(sqrt[5](27))-log _(7)(7)+log _(4)(7)

To solve this expression, we can use the properties of logarithms:<br /><br />1. $ln(e^{6}) = 6$<br />2. $log_{2}(\sqrt[5]{2+}) = log_{2}(2^{1/5}) = 1/5$<br />3. $log_{6}(4) = log_{6}(2^2) = 2log_{6}(2) = 2*1/2 = 1$<br />4. $log_{3}(2) = log_{3}(2) = 1$<br /><br />Therefore, the final result is:<br /><br />$6 + 1/5 - 1 + 1 = 5.2$