Question

Please answer no. 2 and 3.

Answer 1

Step-by-step explanation:

$question \: \: \: no \: \: \: \: 2) \\ \\ 3 + log_{10}(x) = 2 log_{10}(y) \\ 3 = log_{10}( {y}^{2} ) - log_{10}(x) \\ \\ 3 = log_{10}( \frac{ {y}^{2} }{x} ) \\ \\ \frac{ {y}^{2} }{x} = {10}^{3} \\ \\ {y}^{2} = 1000x \\ \\ then \: \: x = \frac{ {y}^{2} }{1000} .$

$question \: no \: \: \: 3(i) \\ \\ \\ \\ log_{2}( log_{2}( log_{3}( log_{3 {}^{} }( {27}^{3} ) ) ) ) = log_{2}( log_{2}( log_{3}( log_{3}( log_{3}( {3}^{9} ) ) ) ) ) \\ \\ = log_{2}( log_{2}( log_{3}( 9log_{3}(3) ) ) ) \\ \\ = log_{2}( log_{2}( log_{3}(9) ) ) \\ \\ = log_{2}( log_{2}(2) ) \\ \\ = log_{2}(1) \\ \\ = 0. \\ \\ \\ \\ \\ question \: no \: 3 \: \:( ii) \\ \\ \\ \\ \\ \\ log_{3}(4) \times log_{4}(5) \times log_{5}(6) \times log_{6}(7) \times log_{7}(8) \\ \\ = \frac{ log(4) }{ log(3) } \times \frac{ log(5) }{ log(4) } \times \frac{ log(6) }{ log(5) } \times \frac{ log(7) }{ log(6) } \times \frac{ log(8) }{ log(7) } \\ \\ = \frac{ log(8) }{ log(3) } \\ \\ = \frac{3 log(2) }{ log(3) } \\ \\ = 3 log_{3}(2)$