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I'm not actually sure how to type this out, so I took a screenshot. Does anyone know how to solve this? http://prntscr.com/5a6cz7

 Nov 26, 2014

Best Answer 

 #2
avatar+99279 
+10

Good answer anon although not many calcs do base three so you cannot just plug the numbers in and get an answer.    

 

I am going to write the question sightly differently

$$\\If\;\;\;y=log_{\textcolor[rgb]{0,1,0}3}3^6\\
then\\
3^6=\textcolor[rgb]{0,1,0}{3}^y\\\\
$Now it is very easy to see that y=6$\\
$so$\\
log_33^6=6\\\\\\
$Remember: $\quad \boxed{If \quad y=log_ba\quad then \quad a=b^y}\\\\
$ You say this as \qquad y=log a base b$\\\\
$Also remember : $\boxed{\mbox{A log is a power}}$$

.
 Nov 26, 2014
 #1
avatar
+5

The log to base 3 of any number is the power numeral when you express that number as a power of 3.

For example, if we write 9 as $${{\mathtt{3}}}^{{\mathtt{2}}}$$ then you see the power there is 2, so when we take logs to base 3,

we write log 9 = 2

 

Summarising, log $${{\mathtt{3}}}^{{\mathtt{2}}}$$ = 2

 

so log $${{\mathtt{3}}}^{{\mathtt{6}}}$$ = ......

what answer do you get? 

If ever you're not sure your answer s right, you can always check using a calculator!

 Nov 26, 2014
 #2
avatar+99279 
+10
Best Answer

Good answer anon although not many calcs do base three so you cannot just plug the numbers in and get an answer.    

 

I am going to write the question sightly differently

$$\\If\;\;\;y=log_{\textcolor[rgb]{0,1,0}3}3^6\\
then\\
3^6=\textcolor[rgb]{0,1,0}{3}^y\\\\
$Now it is very easy to see that y=6$\\
$so$\\
log_33^6=6\\\\\\
$Remember: $\quad \boxed{If \quad y=log_ba\quad then \quad a=b^y}\\\\
$ You say this as \qquad y=log a base b$\\\\
$Also remember : $\boxed{\mbox{A log is a power}}$$

Melody Nov 26, 2014

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