1. Logarithms, Exponentials, Many questions!

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:

2. Originally Posted by bickitrainer
I need help on these questions:

Calculate the exact value of H if:

logH = (log2^1/2) / log2

http://www.mathhelpforum.com/math-help/urgent-homework-help/60945-logarithm-help.html

you will realise that log H = 1/2 => H = ..... This question is indentical to number 8 below.

Also, I scanned these that I don't understand:

..

3. Originally Posted by mr fantastic
..
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.

4. 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:

$\displaystyle 10^{\log(P)}=10^{-\frac35\cdot \log(t) + 3}$

$\displaystyle P=1000\cdot t^{-\frac35}~\implies~P=\dfrac{1000}{\sqrt[5]{t^3}}$