Natural Logs+Calc related question

  • Thread starter JenniferBlanco
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In summary, the student was trying to solve for y in a equation where there was an x in the equation, but they got lost and couldn't figure out how to do it.
  • #1
JenniferBlanco
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Hi,

Can someone please help me out and guide me?

Homework Statement



http://img167.imageshack.us/img167/3892/dscn8321rn1.jpg

Homework Equations


Shown above

The Attempt at a Solution



a) f(x) = -2 +ln(x)^2
f'(x)= 2/x
Ans: All real numbers except for 0

b) -2 +ln (x)^2 =0
ln(x)^2= 2
e^2=x^2
Ans: x = +-e

c) I have no idea how to do this. Do I have to differentiate?-Jen
 
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  • #2
JenniferBlanco said:
Hi,
c) I have no idea how to do this. Do I have to differentiate?
How would you find the "slope of a line that is tangent to the graph"? Once you have the slope, what point would lie on the tangent line if it is tangent to the graph? Once you have the slope, and a point, how do you get the equation of the line?
 
  • #3
Mathdope said:
How would you find the "slope of a line that is tangent to the graph"? Once you have the slope, what point would lie on the tangent line if it is tangent to the graph? Once you have the slope, and a point, how do you get the equation of the line?

OK, so I differentiated the equation and got 2/x
Then I plugged 1 into x, so our slope is 2 while the y value is --> -2 + 0 = -2

and the equation i got is --> y+2=2(x-1)

is that right? Also, are my first two parts right?

-Jen
 
  • #4
Looks like you're all set on this problem!
 
  • #5
Thanks Mathdope and dynamicsolo!
 
  • #6
JenniferBlanco said:
b) -2 +ln (x)^2 =0
ln(x)^2= 2
e^2=x^2
Ans: x = +-e

This part is wrong. If the problem were ln(x2)= 2 then taking the exponential of both sides would give you x2= e2. However, the problem is [ln(x)]2= 2. You need to take the square root of both sides first, then the exponential: ln(x)= [itex]\pm\sqrt{2}[/itex] so x= [itex]e^\sqrt{2}[/itex] or x= [itex]e^{-\sqrt{2}}[/itex].
 
  • #7
Halls, the OP seemed to be the problem you mention but the original image that she uploaded was the other one, so I think it's ok. The poster just needs a bit more care in where parentheses go.
 
  • #8
Mathdope said:
Halls, the OP seemed to be the problem you mention but the original image that she uploaded was the other one, so I think it's ok. The poster just needs a bit more care in where parentheses go.

Jeez, I didn't even look that closely at what was typed. I was looking at the attachment, so I based my assessment of OP's answers on that version of the problem. (I should be watching what students are typing, but since their answers were correct for the correct statement of the equation, I thought it reasonable that they knew what they were doing...)
 

1. What is the purpose of natural logs in scientific calculations?

Natural logs, or ln, are used to find the exponential growth or decay rate of a given variable. This is important in many scientific fields, such as biology, chemistry, and physics.

2. How do you solve logarithmic equations using a calculator?

To solve logarithmic equations using a calculator, you must first input the logarithm function into the calculator, then input the variable and solve for the unknown variable. For example, to solve ln(x) = 4, input ln(x) into the calculator, then input 4 for the answer.

3. What is the difference between natural logs and common logs?

The main difference between natural logs and common logs is the base of the logarithm. Natural logs have a base of e, while common logs have a base of 10. This means that natural logs are used for exponential functions that involve the constant e, while common logs are used for exponential functions that involve the number 10.

4. Can natural logs be negative?

No, natural logs cannot be negative. The domain of natural logs is restricted to positive numbers only, as the natural log of a negative number is undefined. This is because the inverse of an exponential function only exists for positive values.

5. How are natural logs used in scientific data analysis?

Natural logs are commonly used in scientific data analysis to transform data that follows an exponential pattern into a linear pattern. This makes it easier to analyze and interpret the data, as linear relationships are easier to understand and work with. Additionally, natural logs are used in regression analysis to fit a line of best fit for data that follows an exponential trend.

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