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]
