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

Guest Nov 26, 2014

#2**+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}}$$

Melody
Nov 26, 2014

#1**+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!

Guest Nov 26, 2014

#2**+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