Question

Express as a logarithm of a single number or expression.

1/2(logbx - logby)

I went as far as (logb x/y)^1/2 but I'm not sure if this is correct. If it is, where would I go from here?

Answer 1

Be careful with your brackets.
The 1/2 power is being applied to the `contents` of the log, not the log itself.
\[\Large\bf\sf \frac{1}{2}\left(\log_bx - \log_by\right)\quad=\quad \frac{1}{2}\log_b\frac{x}{y}\]
\[\Large\bf\sf =\quad \log_b\left(\frac{x}{y}\right)^{1/2}\]And recall that the 1/2 power is the square root, so `if you wanted to`, you could write it as,\[\Large\bf\sf \log_b\sqrt{\frac{x}{y}}\]

Answer 2

Looks like you're on the right track! :)
Just be careful with your brackets.
That's as far as it can be simplified.

Answer 3

Thank you very much! I'll make sure to watch my brackets next time.

Answer 4

Oh and,

\(\Large\bf \color{#008353}{\text{Welcome to OpenStudy! :)}}\)

Answer 5

Haha, thanks! :D