Verified answer

Using the properties of log:

log a + log b = log(ab)

log a - log b = log(a/b)

alogb = log(b^a)

2log(x) - 4log(3*sqrt(x)) - 1/2 log(x^(3/2))

= log [(x^2)/[(81x^2)(x^(3/4))]]

log x - 2(log y + 3 log z) => From the logarithmic expression above, do away with the bracket via in basic terms multiplying, i.e. log x - 2*log y + 2*3 log z log x - 2 log y + 6 log z => via grouping valuable words together in the above expression, you may desire to have log x + 6 log z - 2 log y => From the guidelines of logarithms, a log b = log b^a, because it extremely is ideal to 6 log z & 2 log y, i.e. log x + log z^6 - log y^2 => From the guidelines of logarithms, log a + log b - log c = log [(ab)/c], then log [(x+z^6)/y^2] as a manner to comprehend this calculation, you may desire to study extra with regard to the guidelines of logarithms.