I need help on these questions:
Calculate the exact value of H if:
logH = (log2^1/2) / log2
Also, I scanned these that I don't understand:
If you are having trouble reading these, please tell me.
I have time for the first scanned page:
6. a) $\displaystyle 10^{\log P} = 10^{2 + \log x} = 10^2 \, 10^{\log x} \Rightarrow P = 100 x$.
6. b) Use the fact that $\displaystyle \log_A B = C \Rightarrow A^C = B$.
7. a) Linear therefore $\displaystyle y = mx + c$ where $\displaystyle y = \log P$ and $\displaystyle x = \log t$.
7. b) See 6. a).
8. Dealt with in post #2.
9. $\displaystyle \log_{10} 5^x = \log_{10} 2^{x + 4} \Rightarrow x \, \log_{10} 5 = (x + 4) \, \log_{10} 2 = x \, \log_{10} 2 + 4 \log_{10} 2$.
Now use algebra to re-arrange to make x the subject. Then use a calculator to get a final answer to the required accuracy.
to #7:
Probably I didn't understand the question but in my opinion you get:
1. From the diagram:
$\displaystyle \log(P)=-\dfrac35\cdot \log(t) + 3$
2. Now the question asks to find a law connecting P and t
Therefore:
$\displaystyle 10^{\log(P)}=10^{-\frac35\cdot \log(t) + 3}$
$\displaystyle P=1000\cdot t^{-\frac35}~\implies~P=\dfrac{1000}{\sqrt[5]{t^3}}$