Final answer:
To find an expression in terms of x and y for y * log₃(1 - 2), rewrite the logarithms using the properties of logarithms. Substitute the expressions for x and y and use the properties of logarithms to simplify the expression. The expression in terms of x and y for y * log₃(1 - 2) is y * log₃(2).
Step-by-step explanation:
To find an expression in terms of x and y for y * log₃(1 - 2), we need to rewrite the logarithms using the properties of logarithms. First, let's rewrite log₉(5) = x as 9^x = 5. Using the property of logarithms, we can rewrite log₂₇(6) = y as 27^y = 6. Now let's substitute these expressions into y * log₃(1 - 2).
Using the property log(xy) = log(x) + log(y), we can rewrite log₃(1 - 2) as log₃(1) + log₃(-2). Since log₃(1) = 0, we can simplify the expression to y * (0 + log₃(-2)). Now, using the property of logarithms log(a^b) = b * log(a), we can rewrite log₃(-2) as log₃((-1) * 2). This gives us y * (0 + log₃(-1) + log₃(2)).