help fast, ​please A. Expand the following and state the Law that is indicated.1. log4(3x)2. log3(27/x)3. log4(x5)

ANSWER1. [tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]2.[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]3.[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) [/tex]EXPLANATION1. The given logarithmic expression is [tex] log_{4}(3x) [/tex]Use the product rule: [tex] log_{a}(mn) = log_{a}(m) + log_{a}(n) [/tex]We apply this rule to obtain:[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]2. The given logarithmic expression is[tex] log_{3}( \frac{27}{x} ) [/tex]We apply the quotient rule:[tex]log_{a}( \frac{m}{n} ) = log_{a}(m) - log_{a}(n) [/tex]This implies that;[tex]log_{3}( \frac{27}{x} ) = log_{3}(27) - log_{3}(x) [/tex]We simplify to get;[tex]log_{3}( \frac{27}{x} ) = log_{3}( {3}^{3} ) - log_{3}(x) [/tex]Apply the power rule:[tex] log_{a}( {m}^{n} ) = n log_{a}(m) [/tex][tex]log_{3}( \frac{27}{x} ) = 3 log_{3}( {3}) - log_{3}(x) [/tex]simplify;[tex]log_{3}( \frac{27}{x} ) = 3 (1) - log_{3}(x) [/tex][tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]3. The given logarithmic expression is;[tex] log_{4}( {x}^{5} ) [/tex]Apply the power rule of logarithms.[tex]log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]This implies that,[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) .[/tex]