book Maths Puzzle Numerical Ability

I feel stupid asking this question but, Is there a differnce between a logarithm of a product and the product of a logarithm? If there is a differnce can you explain it to me?

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book Other Question

Given an unlimited supply of red, white, and green jellybeans, in how many ways can 10 jellybeans be selected?

a) without restrictions
b)if there nmust be atleast one of each How do u prove this?...Show that 3 divides n^3-n for all positive integers n. And does 4 divide n^4-n for all positive intgers n? AND i need to use proof by induction i think, i get the first part but then get stuck at the end...please help