Question

plzzz solve it fast no. 22 in the following image through logarithm

Answer 1

3log( x²y) = 4 + 2logx - logy

3log( x²y ) = 4 + log(x²) - logy

log(x²y)³+ logy - log(x²) = 4

log{ x^6y³× y /x² } = log4

log( x⁴y⁴ ) = log4

x⁴y² = 4

x²y² = ±2

x²y² = 2

xy = ±√2

but , x , y > 0
so,
xy = √2
y = √2/x

and
again,

x - y = 2√6

x - √2/x = 2√6

x² -2√6x -√2 = 0

x = { 2√6 ±√( 24 + 4√2)}/2

= √6 ± √(6 +√2)

but x > 0 so,

x = √6 + √( 6 +√2)

and y = √2/x = √2/( √6 +√(6 +√2)