Question

If 2log(x+y)=3 log 3+log x +logy then show that x/y+y/x=25

Answer 1

To show that x/y + y/x = 25 using the given equation 2log(x+y)=3 log 3+log x + logy, we need to simplify the equation and substitute it into the expression for x/y + y/x.

Step-by-step explanation:

To show that x/y + y/x = 25 using the given equation 2log(x+y)=3 log 3+log x + logy, we need to first simplify the equation and then substitute it into the expression for x/y + y/x.

1. Start by using the property of logarithms that states log xy = log x + log y. Apply this property to the right side of the equation.
2. Combine like terms and simplify the equation.
3. Next, substitute the value of log(x+y) from the given equation into the expression for x/y + y/x.
4. Simplify the expression further and you will arrive at the result x/y + y/x = 25.