How Do You Solve the Equation log(x) = 2cos(x) in the Interval 0 < x < 2π?

  • Thread starter Thread starter ms. confused
  • Start date Start date
AI Thread Summary
To solve the equation log(x) = 2cos(x) in the interval 0 < x < 2π, graphical methods are suggested to identify the intersection points of the two functions. The problem is classified as a transcendental equation, indicating it cannot be solved analytically. Participants discuss using numerical methods to find solutions, particularly since it is presented as a multiple-choice question. Suggestions include plugging in the answer choices into a calculator to verify which values satisfy the equation. Ultimately, the discussion emphasizes the need for numerical approaches or graphical analysis to find the correct solutions.
ms. confused
Messages
90
Reaction score
0
How does this question work? It's multiple choice so its one of the following answers.

logx=2cosx, 0<x<2pi

A. 0.17, 0.71
B. 1.38
C. 1.48, 5.07
D. 1.57, 5.11
 
Physics news on Phys.org
Graphical Solution

There is an x (in your domain) where these two functions intersect. Graph them and see. (This is a trancendental equation, by the way.)

-Beth
 
If it's multiple choice, why don't you plug in the values in your calc?

If you want a method, I don't think this can be solved analytically. Do you know any numerical methods?
 
daster said:
Do you know any numerical methods?

That's what I was hoping to find out.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Solving for x in 0 = -1/8 + 3/8 x / (10^2 +x^2)^0.5
Replies
10
Views
3K
How do I solve for the centroid of a function with a given range?
Replies
4
Views
1K
Find the Instantaneous Velocity of D(x) = x + 2cos(x) in (0,2π)
Replies
1
Views
2K
Find the equation y(x) from y(t) & x(t) then find theta max
Replies
22
Views
3K
Few Trigonometric Functions that I can’t solve involving identities? helpp
Replies
13
Views
3K
How Can You Solve a Differential Equation Involving Exponential Drag Force?
Replies
41
Views
5K
MHB Solving trigonometry equations
Replies
4
Views
2K
Solving Trig Equations: 2cos^2(x)+cos(x)-1=0 in the Interval x≥0 and x≤2π
Replies
2
Views
2K
Solve Trig Inequality: 2cos^2(x) + 1 = 3cos(2x) [0,2pi)
Replies
2
Views
2K
How Do You Calculate Forces and Balance a Hanging Cafe Sign?
Replies
18
Views
3K

Hot Threads

Recent Insights

Back
Top