How would you simplify this log expression?

Question

anonymous · Answer

$$2\log_{2} 15-\log_{2} 5+\log_{2} 3$$

ganeshie8 · Answer

use this :-

$\large k \log_b a  =  \log_b a^k  $

ganeshie8 · Answer

$\large 2\log_{2} 15-\log_{2} 5+\log_{2} 3 $

$\large \log_{2} 15^2-\log_{2} 5+\log_{2} 3 $

$\large \log_{2} 225 -\log_{2} 5+\log_{2} 3 $

ganeshie8 · Answer

we can simplify further, any ideas how ? :)

anonymous · Answer

225-5+3=223 ---> new exponent?

ganeshie8 · Answer

hey no... these are logs, 
we must use log rules ok :)

ganeshie8 · Answer

we use below rule next :-

$\large \log_a b - \log_a c   =  \log_z (\frac{b}{c})$

anonymous · Answer

what does z=

ganeshie8 · Answer

sorry its a typo, it should be a

ganeshie8 · Answer

thnks for catching  :)

ganeshie8 · Answer

apply that rule,

$\large \log_{2} 225 -\log_{2} 5+\log_{2} 3$

$\large \log_{2} (\frac{225}{5})+\log_{2} 3$

anonymous · Answer

$$\log_{2} 225-\log_{2} 5= \log_{2} (225/5)$$

ganeshie8 · Answer

yes ! u can simplify the division inside

anonymous · Answer

45

ganeshie8 · Answer

$\large \log_{2} (\frac{225}{5})+\log_{2} 3 $

$\large \log_{2} 45  +\log_{2} 3 $

ganeshie8 · Answer

next we use this rule :-

$\large  \log_a b + \log_a c  = \log_a bc $

anonymous · Answer

$$\log_{2} 135$$

ganeshie8 · Answer

$\large \log_{2} 45  +\log_{2} 3 $

$\large \log_{2} 45 \times 3  $

$\large \log_{2} 135  $

ganeshie8 · Answer

Yes, thats that final simplified form.

anonymous · Answer

YEAAHHH, thank you!!

ganeshie8 · Answer

there are oly few log rules we need to remember, to do these...

ganeshie8 · Answer

np :) you're wlcme !