Question

Suppose x and y are positive numbers such that log2(x + y) = log2y + 10. Then the correct relation is
A. x = 1023y
B. y = 1024x
C. x = 210
D. x + y = 2y + 10

Answer 1

Answer:

Let x and y be two real numbers, such that 2ln (x-2y) = log x + log y. What is the possible value of (x/y)?

2ln(x-2y) = logx + logy

by natural logarithm rules

aln(x) = ln(x^a)

and product rule lnx + lny = ln(xy)

therefore the given problem now becomes

ln(x-2y)^2 = log(xy)

(x-2y)^2 = xy

x^2 + 4y^2 - 4xy = xy

dividing the equation with xy gives

(x/y) + 4(y/x) -4 = 1

now let t= x/y

t + 4/t - 5 =0

t^2 -5t + 4 = 0

solving this quadratic equation we get

t = x/y = 1 and 4