i'm having trouble solving a few of these logarithm problems

1) If loga2 = logb16, show that b=a^4

i'm also having trouble with squaring logs...for example one of the questions was:

(log10x)^2 - 2log10x + 1 = 0

the answer is 10, but i keep ending up canceling out bothxs

the last one was(2log2x)^2 - 3log2x - 10 = 0

how exactly do you end up with two values for x in that example? the answers are x = 4, 2^(-5/4)

thanks!!