Question

Write as a single logarithm 3-1/2(log6+log3-3log2)

Answer 1

Answer in document below.

Answer 2

`3-(1)/(2)\left(\log6+\log3-3\log2\right)=\\ \log10^3-(1)/(2)\left(\log\left(6\cdot3\right)-\log2^3\right)=\\ \log1000-(1)/(2)\left(\log18-\log8\right)=\\ \log1000-(1)/(2)\left(\log(18)/(8)\right)=\\ \log1000-(1)/(2)\left(\log(9)/(4)\right)=\\ \log1000-\log\left((9)/(4)\right)^{(1)/(2)}=\\ \log1000-\log\sqrt{(9)/(4)}=\\ \log1000-\log(3)/(2)=\\ \log(1000)/((3)/(2))=\\ \log\left(1000\cdot(2)/(3)\right)=\\ \log(2000)/(3)`