Question #f472a

1 Answer
Jun 9, 2015

z= y/(3y/x+3/2)

Explanation:

First, you want to turn the x, y and z powers into factors. To do so, use the naperian logarithm:

color(gray)(Note: ln(a*b) = ln(a)+ln(b) and ln(a^b) = bln(a))

ln(2^x) = ln(3^y) = ln((24sqrt3)^z)

= xln(2) = yln(3) = zln(24sqrt3)

Then, isolate z:

z = (yln(3))/(ln(24sqrt3)) = (yln(3))/(ln(3*2^3)+ln(3^(1/2)))

= (yln(3))/(3ln(2)+ln(3)+ln(3)/2)

Replace ln(2) with y/xln(3)

z= (yln(3))/(3y/xln(3)+ln(3)+ln(3)/2)

= (ycancel(ln(3)))/((3y/x+1+1/2)cancel(ln(3))) = y/(3y/x+3/2)