Find a quadratic polynomial whose sum and product respectively of

Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If it is​ not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.
$g(x)=3-\frac{x^2}{4}$

Logarithmus to simple subtraction - how?
I am learning for a math exam and have the following solution:
$$\begin{gathered} 0.01={0.5}^n \\ n\cdot \log 0.5=\log 0.01 \\ n=\frac{\log 0.01}{\log 0.5} \end{gathered}$$
OK, so far, so good. (I guess)
But now, it gets weird:
$n=\frac{\log 0.01}{\log 0.5}=\frac{0-2}{0.7-1}=\dots$
Can somebody please explain how to go from $\log 0.01$ to $0-2$ and from $\log 0.5$ to $0.7-1$

How does $7\log (8x)=7\ln 8x$
I was working on some math homework with a program called scientific notebook. I was check that
I was writing something correctly.
The original equation is $(\log (x^4)+\log (x^5))/\log (8x)=7$
I then converted it to $\log (x^{(4+5)})=7\log (8x)$
I was expecting to get $\log ((8x{)}^7)$ when I entered the $7\log (8x)$ into the program to evaluate. Can someone please explain this to me?

Solve by factorization
${\displaystyle 6x^2+x-2=0}$

Prove that the chord joining the points P(cp , c/p) and Q(cq ,c/q) on the rectangular hyperbola $xy=c^2$ has the equation pqy + x = c(p + q). Given that the points P, Q and R lieon the hyperbola $xy=c^2$, prove that:
(a) if PQ and PR are inclined equally to the coordinate axes,then QR passes through O,
(b) if angle QPR is a right anglr, then QR is perpendicular tothe tangent at P.

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. ${\displaystyle \frac{3}{4}(t-2)-\frac{2}{5}(2t-3)=\frac{1}{5}}$

${\displaystyle \text{Condense the following expression into a single logarithm using the properties of logarithms. Assume x>0 and }x\ne 6}$
${\displaystyle {\log }_5(x^2-8x+12)-2{\log }_5(x-6)}$