Is log4(18) an Irrational Number?

  • Thread starter Thread starter CPatCU
  • Start date Start date
  • Tags Tags
    Irrational
AI Thread Summary
To determine if log4(18) is an irrational number, the discussion focuses on the definition of rational numbers, which are expressed in the form x/y. The equation log4(18) can be rewritten using the change of base formula: log4(18) = log2(18) / log2(4). The attempt at a solution involves setting log2(18) equal to a rational expression, leading to the realization that a proof by contradiction is necessary. The main challenge lies in demonstrating that assuming log4(18) is rational leads to an inconsistency.
CPatCU
Messages
2
Reaction score
0

Homework Statement


log418
rational numbers are in form x/y


Homework Equations


logab = logcb / logca


The Attempt at a Solution


log218 / log218 = x/y
(b) log218 = (a) log218
log218b = log218a

Then I am stuck.
 
Physics news on Phys.org
Sorry, the problem is prove that log(4)18 is irrational. I also realize that this should be done as a contradiction, I am just not sure how to do it.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Irrational Number Raised To Irrational Number
Replies
30
Views
2K
Is a+b necessarily irrational?
Replies
2
Views
2K
I Is the Ratio of Circumference to Radius of a Circle Always Irrational?
Replies
19
Views
2K
Irrational Numbers a and b used in various expressions
Replies
13
Views
2K
What Are the Different Types of Numbers and How Can You Determine Them?
Replies
8
Views
1K
Is (x+sqrt(2)) or (-x+sqrt(2)) rational?
Replies
2
Views
3K
Is the sum of a rational number and an irrational number always irrational?
Replies
8
Views
2K
Maximum electric field from a blob
Replies
7
Views
720
Torque before slipping in a refrigerator
Replies
3
Views
1K
Proving something is irrational
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top