I have 4 logarithmic problems that I need help with...



log10 (10^1/2)



log10 (1/10^x)



log 3 x^2=2log3 4- 4log3 5



2 log4 9- log2 3

The first one is essentially an identity and quite obvious. Hint for #2 ; rewrite it as log((10^-1)^x). For #3, start by simplifying the 2log3 4- 4log3 5 part by applying the 3rd and 2nd laws of logarithms, in that order. Then, since logarithms are one-to-one, make the arguments equal and go from there. Do #4 in a similar manner ; law #3, followed by law #2.