Question

Express A in terms of others:

2 log A – log S = log (S – a) + log (S – b) + log (S – c)

Answer 1

We are given:

2 log A – log S = log (S – a) + log (S – b) + log (S – c)

Step 1: Combine both sides

Left side:

`2 log A - log S = log A^2 - log S = log (A^2/S)`

Right side:

log (S – a) + log (S – b) + log (S – c) = log [(S – a)(S – b)(S – c)]

Now the equation becomes:

`log(A^2/S) = log[(S - a)(S - b)(S - c)]`

Step 2: Equate the arguments

`A^2/S = (S - a)(S - b)(S - c)`

Multiply both sides by S:

`A^2 = S(S - a)(S - b)(S - c)`

⇒ `A = sqrt(S(S - a)(S - b)(S - c))`