anonymous
  • anonymous
Solve for x. log(x) + log(x - 3) = 1 Please explain how you got the answer.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Nnesha
  • Nnesha
familiar with log rules ?
anonymous
  • anonymous
No I forgot them. That's why I need help with this. Can you help me?
Nnesha
  • Nnesha
quotient rule\[\large\rm log_b y - \log_b x = \log_b \frac{ x }{ y}\] 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 \[\large\rm log_b x^y = y \log_b x\]

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Nnesha
  • Nnesha
so there is a plus sign which rule you should apply ?
anonymous
  • anonymous
addition ----> multiplication
anonymous
  • anonymous
How do you know which number is b?
Nnesha
  • Nnesha
yep so change addition to multiplication log is same so you can apply it
Nnesha
  • Nnesha
b is base
Nnesha
  • Nnesha
so log is same as log base 10 \[\huge\rm log = \log_{10}\]
anonymous
  • anonymous
So is it log(x*(x-3))?
anonymous
  • anonymous
Or log(x^2-3x)?
Nnesha
  • Nnesha
yep right!!
anonymous
  • anonymous
So what do you do with the 1?
Nnesha
  • Nnesha
now you have \[\huge\rm log (x^2 -3x) =1\] next step convert log to exponential form
anonymous
  • anonymous
How do you do that again?
Nnesha
  • Nnesha
and here is the example |dw:1438129295617:dw|
Nnesha
  • Nnesha
remember log = log base 10
anonymous
  • anonymous
\[10^{1} = x ^{2}-3x\]
anonymous
  • anonymous
Is that what I needed to do?
Nnesha
  • Nnesha
yep!!
anonymous
  • anonymous
So then \[x ^{2}-3x-10\] is the next step.
anonymous
  • anonymous
Then I have to factor right?
Nnesha
  • Nnesha
yep
Nnesha
  • Nnesha
gtg :( sorry i'm sure u know how to factor quadratic equation
anonymous
  • anonymous
So x= -2, 5?
anonymous
  • anonymous
Yes but I just want to verify real quick.
Nnesha
  • Nnesha
yep right
anonymous
  • anonymous
Okay Thanks!
Nnesha
  • Nnesha
wait
anonymous
  • anonymous
What? Did I mess up?
Nnesha
  • Nnesha
nope you are right x+2 and x-5 2 times -5 = -10 -5+2 = -3 PERFECT! SO x=-2 , x=5
Nnesha
  • Nnesha
GREAT WORK!
anonymous
  • anonymous
Yay! Thanks again!
Nnesha
  • Nnesha
my pleasure really glad 2 help :=) smart!

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