Question

Solve 19 the one
Kindly NO SPAM​

Answer 1

Solution :

Given :

=> log x = m + n -------------(1)

And,

=> log y = m - n ------------(2)

To Find :

= log 10x/y²

= log 10 • x - log y²

= log 10 + log x - 2 log y

Put the value of (1) and (2) :

= 1 + m + n - 2( m - n )

= 1 + m + n - 2m + 2n

= 1 + m - 2m + n + 2n

= 1 - m + 3n

So, the required answer is (a).

Answer 2

$GOOD \: MORNING \: \\ \\ log(x) = m \: + \: n \: ...Equation \: \: (i) \\ \\ log(y) = m - n \: ...Equation \: \: \ \: \: (ii) \\ \\ add \: both \: the \: equations \: we \: have \\ \\ log(x) + log(y) = 2m...Equation \: \: \: (iii) \\ \\ subtract \: both \: the \: equations \: we \: have \\ \\ log(x) - log(y) = 2n...Equation \: \: \: (iv) \\ \\ now \: add \: equation \: \: iii \: and \: iv \: \: we \: get \\ \\ 2 log(x) = 2m + 2n \\ \\ log(x) = m + n \\ \\ find \: \: \: \: log(10x \div y {}^{2} ) = \\ log(10) + log(x) - 2log(y) \\ \\ log(10 x \div y {}^{2} ) = 1 + (m + n) - 2(m - n) \\ \\ log(10x \div y) = 1 + 3n - m$