Math Help - Someone please help me with the answers to these qeustions logarithms factorising!!!

here are the qeustions on this picture, please help me please!! Logaritmhs and factorising

2. Re: Someone please help me with the answers to these qeustions logarithms factorising

Hello, Jordannn1994!

$2\;\text{Simplify:}$

$(a)\;\log(d^4) - 2\log\sqrt{d} + 3\log(d^2)$
$\log(d^4) - \log(\sqrt{d})^2 + \log(d^2)^3 \;=\;\log(d^4) - \log(d) + \log(d^6)$

. . $=\; \log\left(\frac{d^4\cdot d^6}{d}\right) \;=\;\log(d^9) \;=\;9\log(d)$

$(b)\;\frac{2\log(x^5) - 3\log(x^2)}{2\log(x^2)}$
$\frac{\log(x^5)^2 - \log(x^2)^3}{\log(x^2)^2} \;=\; \frac{\log(x^{10}) - \log(x^6)}{\log(x^4)} \;=\; \frac{\log(\frac{x^{10}}{x^6})}{\log(x^4)} \;=\;\frac{\log(x^4)}{\log(x^4)} \;=\;1$

$(c)\;2\log(p^5) - \log\sqrt[3]{p^9}$
$\log(p^5)^2 - \log(p^9)^{\frac{1}{3}} \;=\;\log(p^{10}) - \log(p^3) \;=\;\log(p^7) \;=\;7\log(p)$

$\text{3. Factor:}$

$(a)\;5pq + 35pr$
$5p(q + 7r)$

$(b)\;12ab - 9bc + 6bd$
$3b(4a-3c+2d)$

$(c)\;5bc - 2bd + 5fc - 2fd$

$b(5c-2d) + f(5c-2d) \;=\; (5c-2d)(b+f)$