Question

Why is...
log root5 = 1/2log 5
log 500 = 3 - log 2
2 - log5 = log20

Thank you! I assume the last two have the same procedure?

Answer 1

\[1) \\log \sqrt 5 \implies \log (5)^{1/2} \implies \frac 12 \log 5\]
^power rule
\[2) \;\log 500 \implies \log \left(\frac{1000}{2} \right) \implies \log 1000 - \log 2 \implies \log 10^3 - \log 2 \]\[\implies 3\log 10 - \log 2 \implies 3 - \log 2\]
^quotient law + power law
\[3) \; 2 - \log 5 \implies 2 \log 10 - \log 5 \implies \log 10^2 - \log 5 \implies \log 100 - \log 5 \]\[\implies \log \left(\frac{100}{5} \right) \implies \log 20\]
^quotient law + power law

does that help?

Answer 2

Yesssssss thank you so much! :)

Math in a different language is pretty tough ;(

Answer 3

yes i agree

Answer 4

took me three takes of math to finally pass algebra :/

Answer 5

Wow I better try super hard then..
I've been studying math in Japanese for four years and after four years of hard core Japanese Im studying math in an English (IB) curriculum x(

I have one last question, how did you know to make log 500 log1000/2 ?
Is that something you just have to realize?

Answer 6

wow cool. japanese.

Answer 7

and yes that was something you have to realize

Answer 8

...i honestly cannot explain how to do it...lol

Answer 9

No problem, just means I have to get a hang of logs and I should be okay. (Hopefully, haha)