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

Actualizada: hace 1 semana:Thank you all!!

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## Answers & Comments

## Verified 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)]

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.

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)

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))

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)