[tex]1) log_{2}(7x + 3) = 1 \\ 7x + 3 = {2}^{1} \\ 7x + 3 = 2 \\ 7x = - 1 \\ x = - \frac{1}{7} [/tex]
[tex]2)5x + 3 = 2x + 7 \\ 5x - 2x = 7 - 3 \\ 3x = 4 \\ x = \frac{4}{3} [/tex]
[tex]3) log_{5}(x) + log_{ {5}^{2} }(x) = 6 \\ log_{5}(x) + \frac{1}{2} log_{5}(x) = 6 \\ \frac{3}{2} \times log_{5}(x) = 6 \\ log_{5}(x) = 4 \\ x = {5}^{4} \\ x = 625[/tex]
[tex]4) log_{ {2}^{3} }(x) + log_{ {2}^{4} }(x) = 12 \\ \frac{1}{3} log_{2}(x) + \frac{1}{4} log_{2}(x) = 12 \\ \frac{7}{12} log_{2}(x) = 12 \\ log_{2}(x) = \frac{144}{7} \\ x = {2}^{ \frac{144}{7} } \\ x = \sqrt[7]{ {2}^{144} } \\ x = {2}^{20} \times \sqrt[7]{ {2}^{4} } [/tex]
