Final answer:
Logarithms of certain numbers can be expressed in terms of log 2 (x) and log 3 (y). For log 18, it is written as x + 2y, while log 9 is expressed as 2y based on the properties of logarithms.
Step-by-step explanation:
If log 2 = x and log 3 = y, we can express other logarithms in terms of x and y using properties of logarithms.
For log 18:
18 can be expressed as 2 × 9, which is 2 × 3². Using the property of logarithms that the logarithm of a product equals the sum of the logarithms, and the logarithm of a power equals the exponent times the logarithm, we have:
log 18 = log (2 × 3²) = log 2 + log 3² = log 2 + 2 log 3 = x + 2y.
For log 9:
9 is 3², so again using the property that the logarithm of a power equals the exponent times the logarithm:
log 9 = log 3² = 2 log 3 = 2y.