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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 weeks ago

Can someone help me with this equation? Reducing to linear form using logs?

T = 2π√(l/g)

Hi there. I need some math help.

I think I have it but I'm not sure I'm trying to study on my own and teach myself i worked it out but I'm not 100% and I hope someone out there can help me out so I can see what they do and how to approach these

Thanks a ton you'll save me from going into debt with tutors 

Update:

@Puzzling @Alan

I really did work it out myself but I don't think I did it right because I was confused by some of it. You're both so helpful that explained it better than the videos I was trying to watch on it and anything I've seen online thank you, thank you, thank you!

Update 2:

Thank you all!!

5 Answers

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  • 2 weeks ago
    Favorite Answer

    If you've worked it out, I think you should have posted your work and then asked for someone to review it. Otherwise it looks like you just want someone else to do the work.

    In any case, I'll do my best to help.

    Original equation:

    T = 2π√(l/g)

    Take the log of both sides:

    log(T) = log[2π√(l/g)]

    Use the product rule to turn the log of a product in a sum of logs:

    log(T) = log(2) + log(π) + log[√(l/g)]

    Looking at the third log, we know that a square root can be rewritten as raising something to the ½ power:

    log(T) = log(2) + log(π) + log[(l/g)^½]

    Using the power rule, we can bring ½ to the front:

    log(T) = log(2) + log(π) + ½ log(l/g)

    Finally, use the quotient rule to split the last log into a subtraction of logs.

    log(T) = log(2) + log(π) + ½[log(l) - log(g)]

    Attachment image
  • 2 weeks ago

    T=(2pi)sqr(L/g)

    =>

    log(T)=[log(L)-log(g)]/2+log(2pi)

    =>

    log(T)=log(L)/2+log[2pi/sqr(g)]

    This is a linear equation in "log",

    where "log" are in the base of 10;

    log(L) is the independent variable;

    Log(T) is the dependent variable.

    log[2pi/sqr(g)] is the constant term.

  • 2 weeks ago

    To complete:

    Log[a](x) = Ln(x) / Ln(a) → where a is the base

    Ln(x^a) = a.Ln(x)

    Log(x^a) = a.Log(x)

    Ln(ab) = Ln(a) + Ln(b)

    Log(ab) = Log(a) + Log(b)

    Ln(a/b) = Ln(a) - Ln(b)

    Log(a/b) = Log(a) - Log(b)

    Log(1) = 0

    Ln(1) = 0

    Ln(e) = 1 → e ≈ 2.71828182

    T = 2π√(ℓ/g)

    Ln(T) = Ln[2π√(ℓ/g)]

    Ln(T) = Ln(2π) + Ln[√(ℓ/g)]

    Ln(T) = Ln(2) + Ln(π) + Ln(√ℓ) - Ln(√g)

    Ln(T) = Ln(2) + Ln(π) + Ln[ℓ^(1/2)] - Ln[g^(1/2)]

    Ln(T) = Ln(2) + Ln(π) + (1/2).Ln(ℓ) - (1/2).Ln(g)

  • 2 weeks ago

    T = 2π√(l/g)

    ==> log(T) = log(2π(l/g)^(1/2))

    ==> log(T) = log(2π) + log((l/g)^(1/2))

    ==> log(T) = log(2π) + log(l^(1/2)) - log(g^(1/2))

    ==> log(T) = log(2π) + log(l)/2 - log(g)/2

    2π is a constant

    and I'd assume that g is a constant

    so, rearranging...

    ==>log(T) = log(l)/2 + log(2π/g^(1/2))

  • Alan
    Lv 7
    2 weeks ago

    T = 2π√(l/g)   

    becomes 

    log(T) = log(2π) + (1/2)log(l) - (1/2) log(g)  

    if you consider g a constant , you're not 

    going to other planets or to really high altitudes

    Then, 

    log(T) =  (1/2)log(l)   - log ( 2π/√g)   

    log slope = (1/2)

    constant/intercept  -log( 2π/√g)

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