karmalol1380 karmalol1380
  • 22-10-2019
  • Mathematics
contestada

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.

Respuesta :

mariacsinning mariacsinning
  • 23-10-2019

Answer:

[tex]x=a^{2} -b^{2}[/tex]

Step-by-step 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 [tex]a^{2} -b^{2}[/tex], so:

log(x) =log([tex]a^{2} -b^{2}[/tex])

Finally, [tex]10^{log(m)}=m[/tex], so we can isolate x as:

[tex]10^{log(x)} =10^{log(a^{2}-b^{2})}[/tex]

[tex]x=a^{2} -b^{2}[/tex]

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