Question

If xx> 0, a + b > 0, a > b, and log(x) = log(a + b) + log(a − b), find x in terms of a and b.

Answer 1

`x=a^(2) -b^(2)`

Explanation:

By properties of logarithms we know that:

log(m)+log(n)=log(m*n)

So, we can write the equation as:

log(x) = log(a + b) + log(a − b)

log(x) =log((a+b)(a-b))

If we multiply (a+b)(a-b) we get
`a^(2) -b^(2)`, so:

log(x) =log(
`a^(2) -b^(2)`)

Finally,
`10^(log(m))=m`, so we can isolate x as:

`10^(log(x)) =10^{log(a^(2)-b^(2))}`

`x=a^(2) -b^(2)`