anonymous
  • anonymous
Express as a single logarithm. log6496 – log62 I know logs pretty well but I don't know how to express 2 logs as a single log, can someone please help??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I meant log base 6 of 496 - log base 6 of 2
anonymous
  • anonymous
\[\log_{6} 496-\log_{6} 2=\log_{6} \frac{ 496 }{ 2 }=\log_{6} 248\]
anonymous
  • anonymous
That's what I thought thank you! What about, log base 5 of 50 + log base 5 of 2.5?

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anonymous
  • anonymous
I know it has to equal something in the final answer and that confuses me
Nnesha
  • Nnesha
quotient rule\[\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}\] to condense you can change subtraction to division product rule \[\large\rm log_b x + \log_b y = \log_b( x \times y )\] addition ----> multiplication power rule \[\large\rm log_b x^y = y \log_b x\] you should familiar with these
Nnesha
  • Nnesha
there is a plus sign so which property you should apply ?
anonymous
  • anonymous
the product property
Nnesha
  • Nnesha
yes right
anonymous
  • anonymous
I am doing a test review and all of the multiple choice answers for the question equal something, like one answer is, log base 5 of 125=3
anonymous
  • anonymous
How do you find what it equals?
Nnesha
  • Nnesha
log base 5 of 50 + log base 5 of 2.5 for this question ?
anonymous
  • anonymous
yes
Nnesha
  • Nnesha
\[\huge\rm log_5 50+ \log_5 2.5\] is this ur question ?
anonymous
  • anonymous
yes
Nnesha
  • Nnesha
there isn't an equal sign..
anonymous
  • anonymous
These are the possible answers: \[\log_{5}125=3 \] \[\log_{5}112.5=2.93 \] \[\log_{5}112.5=22.5 \] \[\log_{5}125=625 \]
Nnesha
  • Nnesha
alright then you have to apply the `change of base` formula \[\huge\rm log_b a= \frac{ \log a }{ \log b }\]
Nnesha
  • Nnesha
\[\huge\rm log_5 50+ \log_5 2.5\] first) how would you write this in single log form b applying product property ?
anonymous
  • anonymous
\[\log_{5}125 \] ?
Nnesha
  • Nnesha
yes right now use change of base formula
anonymous
  • anonymous
How do I know what to change the base to?
Nnesha
  • Nnesha
base would stay the same hmm what do you mean ? o.O here is an example \[\log_2 3 =\frac{ \log(3) }{ \log(2) }\]
anonymous
  • anonymous
oh okay! I was looking at my notes and I read the equation wrong!
Nnesha
  • Nnesha
ohh
anonymous
  • anonymous
soooo is the answer \[\log_{5}125=3 \]
Nnesha
  • Nnesha
if log_5 (125) is equal to 3 then yes did you use the formula ?
Nnesha
  • Nnesha
how would you use `change of base formula` for \[\large\rm \log_5 125\]
anonymous
  • anonymous
\[\frac{ \log(125) }{ \log(5) }\]
Nnesha
  • Nnesha
perfect!
anonymous
  • anonymous
Awesome! This makes sense now! Thank you so much! You are very smart
Nnesha
  • Nnesha
glad to hear that & thanks & good job! good luck !
anonymous
  • anonymous
Thanks! :)

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