marcelie one year ago help please !!! How do i solve this without using a calculator. log 6 ((sq 6 )

1. marcelie

|dw:1444007879943:dw|

2. ybarrap

Using the rules for logs: $$y=\log_6{\sqrt 6}=\log_6{ 6^{1/2}}=\cfrac{1}{2}\log_6{ 6}=\cfrac{1}{2}\\$$ Since $$\log_6{ 6}$$ means, what is x such that $$6^x=6$$. Therefore, x=1 and the result follows since $$\log_6{ 6}=1$$ Does this make sense?

3. marcelie

hmm. i solved it liek this .. is this corerct ?|dw:1444008964769:dw|

4. marcelie

nvm i got it lol tyy

5. ybarrap

Be careful, the rule is $$\log a^{1/2}=(1/2)\log a$$

6. marcelie

whats the name of that rule?