This is what I had:
$\displaystyle \log _354 + log_35 - log_84$
$\displaystyle log_33 + log_33 + log_32 + log_35 - log_8(8^\frac{2}{3}) $
$\displaystyle 2\tfrac{1}{3} + log_310 $
is this correct? can I simplify any further?
thanks
This is what I had:
$\displaystyle \log _354 + log_35 - log_84$
$\displaystyle log_33 + log_33 + log_32 + log_35 - log_8(8^\frac{2}{3}) $
$\displaystyle 2\tfrac{1}{3} + log_310 $
is this correct? can I simplify any further?
thanks
$\displaystyle \log_3{54} + \log_3{5} - \log_8{4}$
$\displaystyle = \log_3{(27 \cdot 2)} + \log_3{5} - \log_8{\left(8^{\frac{2}{3}}\right)}$
$\displaystyle = \log_3{27} + \log_3{2} + \log_3{5} - \frac{2}{3}$
$\displaystyle = \log_3(3^3) + \log_3{(2\cdot 5)} - \frac{2}{5}$
$\displaystyle = 3 + \log_3{10} - \frac{2}{5}$
$\displaystyle = \frac{13}{5} + \log_3{10}$.
So yes, you are correct. And no, it can't be simplified any further. The best you could do is to convert it to a base 10 or base $\displaystyle e$.