Answer
See the explanation
Work Step by Step
Law of Logarithms:
1. $\log(AB)=\log A +\log B$
2. $\log(A/B)=\log A -\log B$
3. $\log(A^C)=C\log A$
4. $\log_{A}B=\frac{\log_{C}A}{\log_{C}B}$
Properties of Loagrithms:
1. $\log_{a}1=0$
2. $\log_{a}a=1$
3. $\log_{a}a^x=x$
4. $a^{\log_{a}x}=x$
a. From the law of logarithms 3 and then law of logarithms 1...
$\log a+2\log b=\log a+\log b^2=\log ab^2$
b. From the law of logarithms 2...
$\ln(x^2-25)-\ln (x+5)=\ln \left(\frac{x^2-25}{x+5}\right)=\ln(x-5)$
c. From the law of logarithms 3 and then the law of logarithms 2 and then law of logarithms 1...
$\log_{2}3-3\log_{2}x+\frac{1}{2}\log_{2}(x+1)=\log_{2}3-\log_{2}x^3+\log(\sqrt {x+1})=\log_{2}(3/x^3)(\sqrt {x+1})$
