Question

solve for x to the nearest thousandth:
100 ln (2x-3)-10=102

Answer 1

so is the equation 100(2x-3)-10=102?

Answer 2

yes

Answer 3

So no ln?

Answer 4

wait theres an ln in it before the 2x-3

Answer 5

sorry, the ln is there

Answer 6

Use math properties to isolate x. Start by adding 10 to both sides, then divide by 100 on both sides etc.

Answer 7

okay, then what should i do with the ln?

Answer 8

the ln part confuses me, im not too good with it

Answer 9

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

Answer 10

making -310, with this you should add it to the other side of the = sign

Answer 11

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

Answer 12

but how do i solve for the x?

Answer 13

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

Answer 14

you left out the ln (natural logarithm)

Answer 15

So e^(ln) is 1. So the left side goes to 2x-3. So you should get 2x-3=e^(1.12)

Answer 16

ok, so i set 2x-3=1.12. then i added 3 to 1.12 and got 2x=4.12.

Answer 17

is that right?

Answer 18

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.

Answer 19

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?

Answer 20

Yes!

Answer 21

You can always check by plugging your value of x back into the equation and seeing if it's equal.

Answer 22

yay!! thank you so much!! :)

Answer 23

No problem. :)