Hi I have a homework problem that is always wrong and I dont know which problem I have wrong. Its really annoying since it doesn't indicate which one is wrong, it just says something is incorrect. I have gone through these multiple times and still can't figure it out.
If $\ln a=2$, $\ln b=3$, and $\ln c=5$, evaluate the following:
(a) $$\ln\frac{(a^{3})}{(b^{−3}c^{−4})} = -23$$
(b) $$\ln\sqrt{b^{−2}c^{−3}a^{1}}= -19/2$$
(c) $$\frac{\ln(a^{−1}b^{2})}{ln(bc)^{−1}}= 12$$
(d) $${\ln c^{−2}}{{(\ln\frac{a}{b^{2}}})^{3}}= 640$$
ln a=2, ln b=3, and ln c=5
$\ln\frac{a^3}{(b^{−3})(c^{−4})} = \ln a^3 - \ln ((b^{−3})(c^{−4})) = \ln a^3 -(\ln b^{−3} + \ln c^{−4})= \ln a^3 -\ln b^{−3} - \ln c^{−4} = 3\ln a + 3 \ln b + 4 \ln c = 6 + 9 +20 = 35$
so that one is wrong.
$\ln ((b^{−2})(c^{−3})(a^1))^{1/2} = \frac 12 [-2 \ln b - 3 \ln c + \ln a]= \frac 12 [-6 - 15 + 2] = -19/2$ so that one is right.