The question is
\log_{x}\left({10}\right)+log(x)=2
where (obviously) I have to find x.
I tried changing the base,
$\frac{log(10)}{log(x)}+log(x)=2$
$\frac{1}{log(x)}+log(x)=2$
${log(x)}^{-1}+log(x)=log(100)$
but I could go no further. Whatever I try, I always got a wrong answer.
By guessing...
$\alpha$ and $\beta$ are the roots of the equation $2{x}^{2}-5x+c=0$. If $4\alpha-2\beta=7$, find the value of $c$.
I did the following:
$\alpha+\beta=-\frac{-5}{2}=\frac{5}{2}$
$\alpha\beta=\frac{c}{2}$
$\frac{c}{2}=\frac{7+2\beta}{4}\cdot\frac{-7+4\alpha}{2}$...
After simplification, I found that $\overline{FG}=\frac{5x-1}{1+x}$. Can it be simplified further or is this the final answer? (When I measure the picture it measures nearly excatly $x$ cm):confused:
In the figure, ABCD is a square of side 1 cm. ABFE and CDFG are trapeziums(/trapeziods?). The Area of CDFG is twice the Area of ABFE. Let x cm be the length of AE.
(a) Express the length of FG in terms of x.
(b) Find the value of x, correct to 2 decimal places.
Thanks! :D