linda
  • linda
solve for x to the nearest thousandth: 100 ln (2x-3)-10=102
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
so is the equation 100(2x-3)-10=102?
linda
  • linda
yes
anonymous
  • anonymous
So no ln?

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linda
  • linda
wait theres an ln in it before the 2x-3
linda
  • linda
sorry, the ln is there
anonymous
  • anonymous
Use math properties to isolate x. Start by adding 10 to both sides, then divide by 100 on both sides etc.
linda
  • linda
okay, then what should i do with the ln?
linda
  • linda
the ln part confuses me, im not too good with it
anonymous
  • anonymous
ok, so first im pretty sure that you have to distribute the 100 to the 2 and -3 then you should put the -300 and the -10 together
anonymous
  • anonymous
making -310, with this you should add it to the other side of the = sign
anonymous
  • anonymous
e is the inverse of ln. So if both sides are e raised to a power. You will get e^(ln(2x-3)=e^1.12
linda
  • linda
but how do i solve for the x?
anonymous
  • anonymous
100(2x-3)-10=102 200x-300-10=102 200x-310=102 200x=412 because you added the 210 the the 102 then you should divide 400 by 200 that should leave you with x=2.06
linda
  • linda
you left out the ln (natural logarithm)
anonymous
  • anonymous
So e^(ln) is 1. So the left side goes to 2x-3. So you should get 2x-3=e^(1.12)
linda
  • linda
ok, so i set 2x-3=1.12. then i added 3 to 1.12 and got 2x=4.12.
linda
  • linda
is that right?
anonymous
  • anonymous
No. You left out the e. E is a function in itself just like ln. So you can use a calculator to find the value of e^1.12. Then you can continue with your process.
linda
  • linda
ok, so i got 3.065 for e^1.12. then i added 3 to that. i got 2x=6.065. then i divided by two and got x=3.033. sound right?
anonymous
  • anonymous
Yes!
anonymous
  • anonymous
You can always check by plugging your value of x back into the equation and seeing if it's equal.
linda
  • linda
yay!! thank you so much!! :)
anonymous
  • anonymous
No problem. :)

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