text: i need help with understanding logarithms.  please show work in this sample problem:? express in terms of sums and differences of logarithms. loga4x^2yz^4  express as a single logarithm and, if possible, simplify. 1/2log s + 5 log q if two logs are added, you multiply the things you are taking the log of. if two logs are subtracted, you divide the things you are taking the log of (the positive value in the numerator) if you have a coefficient, it becomes the exponent of the thing you are taking the log of in "factored" form.  i.e.: 1/2logs = log(s^(1/2)  we now know enough to do the problems.  let's do the second one first:  1/2log(s)+5log(q) =  log(s^(1/2))+log(q^5)= log(s^(1/2)q^5)  we're done!  for the first one, we have  log((a)(4)(x^2)(y)(z^4))  i added the parantheses to make it easier to visualize what to do.  we have exponents (make them coefficients) and multiplication (make it addition).  the whole things equals.  log(a) + log(4) + 2log(x) + log(y) + 4log(z)  i hope this is all clear and helps you.