To express log9 in terms of log3 x and log3 y, we need to use the properties of logarithms.
Let's start by expressing log9 in terms of a base of 3:
log9 = log(3^2)
Using the logarithmic property: log(a^b) = b * log(a)
log(3^2) = 2 * log3
Now, we need to express log3 in terms of log3 x and log3 y. Let's assume that x and y are positive numbers.
Using the logarithmic property: log(a * b) = log(a) + log(b)
log3 = log3(x * y)
Finally, we have:
2 * log3 = log9 = log3(x * y)
To solve for x and y simultaneously, we can equate the exponents:
2 = x * y
From this equation, we can solve for x and y.
There are several possible solutions. For example, if x = 2 and y = 1 or x = 1 and y = 2, both of these values would satisfy the equation 2 = x * y.
So, the simultaneous solution for x and y could be x = 2, y = 1 or x = 1, y = 2.