Question

What is the way you could find the "exact" value of the following sum of logarithms: log 3000 + log(1/3)

a.) It doesn't have an exact value, but instead a value approximated with a decimal number
b.) Use the Quotient Property of Logarithms
c.) Find its equivalent value, log 1000
d.) Convert it to its equivalent exponential form

Answer 1

i think it is A but i am not 100%sure

Answer 2

hint: look at this page. Specifically at rule 1

http://www.purplemath.com/modules/logrules.htm

Answer 3

Did I help your girlfriend?????

Answer 4

the rule that multiplication inside the log can be turned into addition outside the log?

Answer 5

Yes, so using that rule

\[\Large \log\left({\color{red}{A}}\right)+\log\left({\color{blue}{B}}\right) = \log\left({\color{red}{A}}*{\color{blue}{B}}\right)\]

\[\Large \log\left({\color{red}{3000}}\right)+\log\left({\color{blue}{\frac{1}{3}}}\right) = \log\left({\color{red}{3000}}*{\color{blue}{\frac{1}{3}}}\right)\]

\[\Large \log\left({\color{red}{3000}}\right)+\log\left({\color{blue}{\frac{1}{3}}}\right) = \log\left(1000\right)\]

Do you see how to finish up?

Answer 6

no I'm not sure I get it

Answer 7

where are you stuck? which step?

Answer 8

Hint: log a = log b = log ab (which jim has already pointed out).

log 5 + log (1/2) = log (5/2).

Please give this homework problem a try.