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

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)