anonymous
  • anonymous
Someone help to explain this please!! log x + log (x + 48) = 2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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campbell_st
  • campbell_st
well using log laws for multiplication the problem can be written as \[\log(x(x + 48)) = 2~~~or~~~~\log(x^2 + 48x) = 2\] if this is a base 10 log system them raise each side of the equation to a power of 10 and you need to know the log law \[a^{\log_{a}(b)} = b\] so \[10^{\log(x^2 + 48x)} = 10^2\] which becomes \[x^2 + 48x = 100\] now you can solve for x and remember you can't take the log of a negative number when you consider the solutions.
Hero
  • Hero
@calecea Any questions about Campbell_st approach here?
anonymous
  • anonymous
@Hero no, I think I got it.

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anonymous
  • anonymous
@campbell_st , so does x=4.9? I did square root to both sides, then added the x and got 49, then divided by 10.
campbell_st
  • campbell_st
well I would rewrite it as \[x^2 + 48x - 100 = 0\] and this factors to (x - 2)(x + 50) = 0 so the solutions seem to be x = 2 and x = -50
anonymous
  • anonymous
oh, I didn't know it was supposed to be written that way.
campbell_st
  • campbell_st
well lets look at the positive value x = 2 you get log(2) + log(2 + 48) this can be rewritten as log(2 x 50) = log(100) and 100 = 10^2 so it seems to make sense
anonymous
  • anonymous
oh ok, Thank you!

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