laws of logarithms

[blitzen]

I know that there is a division rule with the logarithms, but I have a question in regards to if I am correct with this:

If I have the ln (sq rt. [(x+7) / (x-8)] )

Would that give me ln (sq. rt. (x + 7)) - ln (sq. rt. (x - 8)) ?

 

[mmm4444bot]

Yes, for all valid values of x.

If you're savvy with graphing technology, you might have graphed both expressions to verify this identity.



BTW, we can text square-root notation like so:

ln[sqrt({x + 7}/{x - 8})] = ln[sqrt(x + 7)] - ln[sqrt(x - 8)]