Solve the simultenous equation.

Question

XY=160
LogX - 3LogY=1

Answer 1

xy = 160
logx - 3logy = -1

logx + logy = log160
logx - 3logy = -1
subtract to get
4logy = log160 + 1 = log160 + log10 = log1600 = 2log40
logy = 1/2 log40
y = √40
so, x=160/√40 = 4√40

or,

xy = 160
logx - 3logy = -1

xy = 160
x/y^3 = 1/10

x = 160/y, so
160/y^4 = 1/10
y^4 = 1600
y = √40
x = 160/√40 = 4√40

yeah, I know √40 = 2√10 but I think it's easier to see this way.