The laws of logarithm has specific theories to be applied depending on the form of the given expression. Some of it are the following:
alogb = log b^a
log a + log b = log (ab)
log a - log b = log (a/b)
for letter A,
xlogb r + logb s - logb t = logb [(rs)^x]/t
is wrong because the s part from logb s has no x before the logb
for letter B,
xlogb r + xlogb s - logb t = logb (rs/t)^x
is wrong because the t part from logb t has no x before logb
for letter C,
logbr - xlogb s + xlogb t = logb (r)/(st)^x
is correct because after the minus sign, condensing it would form a fraction, the plus sign will form a multiplication and both s and t are raised to the power of x.
So the answer is letter C.
