Maddy1251
  • Maddy1251
Use the rules of logarithms to expand log[(x+3)^4(x-5)^7]
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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Owlcoffee
  • Owlcoffee
Like this? \[\log[(x+3)^{4(x-5)^7}]\]
Maddy1251
  • Maddy1251
\[LOG[(x+3)^{4} (x-5)^{7}]\]
Maddy1251
  • Maddy1251
I should of posted my question and then wrote that out :P

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ninjaslice
  • ninjaslice
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welshfella
  • welshfella
use the following 2 rules log ab = log a + log b and log a^n = n log a
Maddy1251
  • Maddy1251
@welshfella are you saying this\[\log (ab)=\log (x+3)^{4} +\log(x-5)^{7}\]
Owlcoffee
  • Owlcoffee
okay, that makes things easier. \[\log[(x+3)^4(x-5)^7]\] You see, most of the times we want to expand a logarithmic math expression we use the properties of the logarithm. In this case we will use a logarithmic property that involves the product of the internal logarithmands. \[\log_{n} AB=\log_{n} A + \log_{n}B \] Well, in the case of this excercise we can apply it, since the base is 10: \[\log[(x+3)^4(x-5)^7]\] \[\iff \log (x+3)^4+\log(x-5)^7\] This of course is not ready yet, because we still have those exponents, from that we will use the property: \[\log_{n} A^m = m(\log_{n} A)\] So, we can take down those exponents by using this property, which comes in quite useful when dealing with logarithms: \[ \log (x+3)^4+\log(x-5)^7\] \[\iff 4\log(x+3)+7\log(x-5)\]
welshfella
  • welshfella
you are on the way to answering it now you apply the second rrule
welshfella
  • welshfella
OwlCoffee has it
Maddy1251
  • Maddy1251
@welshfella Ah you started and then @Owlcoffee finished. I saw where you were going, it was a matter of taking the exponents after you got it into the first form! So simple..
Maddy1251
  • Maddy1251
@Owlcoffee I will medal you, can you medal @welshfella
welshfella
  • welshfella
yes Not difficult
Maddy1251
  • Maddy1251
@welshfella Thank you!! :)
welshfella
  • welshfella
yw
ninjaslice
  • ninjaslice
I put in the right answer though with my image right?

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