Question

URGENT!!! PLS HELP....

Answer 1

Ex1

`ln( \frac{ {y}^(4) { {e}^(2) } }{ \sqrt[3]{ {x}^(2) } } ) \\ = ln( {y}^(4) {e}^(2) ) - ln( \sqrt[3]{ {x}^(2) } ) \: \: \: \: (by \: quotient \: rue) \\ = ln( {y}^(4) ) + ln( {e}^(2) ) - ln( \sqrt[3]{ {x}^(2) } ) (by \: product \: rule) \\ = 2 + ln( {y}^(4) ) - ln( \sqrt[3]{ {x}^(2) } ) \\ = 2 + 4 ln(y) - (3)/(2) ln(x) \: \: \: \: (power \: rule)`

Ex2

`log_(4)(x + 2) + log_(4)(x - 1) = 1 \\ log_(4)((x + 2)(x - 1)) = 1 \: (by \: product \: rue) \\ log_(4)( {x}^(2) + x - 2 ) = 1 \\ {x}^(2) + x - 2 = {4}^(1) \\ {x }^(2) + x - 6 = 0 \\ x = 3 \: \: or \: x = - 2`