Question

Xy=80 solve log x- log y=1

Answer 1

Question: Solve for x and y in the equation.

xy=80 and log x - 2 log y =1

Answer:

x = 40, y = 2

Explanation:

xy = 80.......................... Equation 1

logx-2logy = 1

logx-logy² = 1

Applying the laws of logarithm,

log(x/y²) = log10

x/y² = 10

x = 10y²......................... Equation 2

Substitute the value of x in therms of y equation 2 into equation 1

10y²(y) = 80

10y³ = 80

y³ = 8

y =
`\sqrt[3]{8}`

y = 2.

Substitute the value of y into equation 1

2x = 80

x = 80/2

x = 40

Therefore,

x = 40, y = 2