Expert: Sherman D. - 10/13/2008

Question
Express log(2root10) -1/3 log(0.8) -log(10/3) in the form c+logd where c and d are rational numbers and the logarithms are to the base 10

answer is log3-1/6 ...........I have the log3 and some other bits,  but am struggling with the -1/3 log (0.8) part of the question."

Answer
log(sqrt(10)) - (1/3)log(.8) - log(10/3) =
log(10^(1/2)) - log((8/10)^(1/3)) - (log(10) - log(3))
(1/2)log(10) - (log(8^(1/3)) - log(10^(1/3))) - (1 - log(3))
(1/2)(1) - (log(2) - (1/3)log(10)) - 1 + log(3)
(1/2) - log(2) + (1/3) - 1 + log(3)
(-1/6) + log(3/2)

i get that unless i went wrong somewhere, or you left out something in the answer, or i misunderstood something you wrote down.