Question

Which of the following is the correct expansion of log2 (2/xy)^3?

a) 3log2(2) - 3log2(x) - 3log2(y)
b) 6log2(2) - 3log2(x) - 3log2(y)
c) 9log2(2) - 3log2(x) - 3log2(y)
d) 3log2(2) - 6log2(x) - 6log2(y)

Answer 1

The correct expansion of log2 (2/xy)^3 is 3log2(2) - 3log2(x) - 3log2(y).

Step-by-step explanation:

The correct expansion of log2 (2/xy)3 is:

3log2(2) - 3log2(x) - 3log2(y)

This is because the exponent rule states that when you have a power raised to another power, you multiply the exponents. In this case, we have (2/xy)3, so the exponent 3 applies to both the numerator and the denominator. Using the logarithm property for division, we can rewrite the expression as log2(23) - log2(x3) - log2(y3). Simplifying further gives us 3log2(2) - 3log2(x) - 3log2(y).