aem9296
  • aem9296
Write as a single logarithm 2ln(5)+ln(4)-3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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AkashdeepDeb
  • AkashdeepDeb
ln means log to the base e Now 2ln5 = ln 25 +ln4 - ln3 Now use log properties Ln A + Ln B = Ln (AB) Ln A - Ln B = Ln (A/B) So your question would equal ln 25 * 4/3 Got it? :)
zepdrix
  • zepdrix
\[\Large 2\ln(5)+\ln(4)-3\] I don't think the last term was supposed to be ln3. Can you confirm that aem? D:
zepdrix
  • zepdrix
Is your problem this:\[\Large 2\ln(5)+\ln(4)-3\]This:\[\Large 2\ln(5)+\ln(4)-\ln(3)\]Or this:\[\Large 2\ln(5)+\ln(4-3)\]

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aem9296
  • aem9296
this first one
zepdrix
  • zepdrix
Then we need to fix one thing :) That last term isn't ln(3). Instead what we'll do is some sneaky math to get a natural log attached to it.
zepdrix
  • zepdrix
Whenever the `insides` of our log match the `base` of our log, then it's equal to 1. Examples:\[\Large \log_2(2)=1\]When no base is written it's a base of 10 right?\[\Large \log(10)=1\] So we can also apply this to the natural log,\[\Large \color{royalblue}{\ln(e)=1}\]
zepdrix
  • zepdrix
\[\Large 2\ln(5)+\ln(4)-3\cdot\color{royalblue}{1}\]We want to be sneaky and multiply our 3 by 1.\[\Large 2\ln(5)+\ln(4)-3\cdot\color{royalblue}{\ln(e)}\]
zepdrix
  • zepdrix
Now all of our terms have logs so we can use rules of logarithms to write them as a single log! :D Akash listed some nice steps above, we'd just need to deal with the 3 term a little differently.
aem9296
  • aem9296
OH okay! :) thanks so much!

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