1. ## Logs

Given that logbase6(2)=0.387, determine the value of logbase6(9)

2. Originally Posted by Tiger
Given that logbase6(2)=0.387, determine the value of logbase6(9)
$\log_{6} (9) = \log_{6} (\frac{18}{2}) = \log_{6} (\frac{ (6)(3) }{ (2) })$
$=\log_{6} (6) + \log_{6} (3) - \log_{6} (2)$
$=\log_{6} (6) + \log_{6} (\frac{6}{2}) - \log_{6} (2)$
$=\log_{6} (6) + \log_{6} (6) - \log_{6} (2) - \log_{6} (2)$
$=1 + 1 - 2 \log_{6} (2)$
$=2 - 2 (0.387)$
$=2 - 0.774$
$=1.226$

3. Hello, Tiger!

A slight variation of the General's solution . . .

Given: . $\log_6(2)\,=\,0.387,\:\text{ determine the value of: }\:\log_6(9)$

$\log_6(9) \;\;=\;\;\log_6\left(\frac{36}{4}\right) \;\;=\;\;\log_6(36) - \log_6(4) \;\;=\;\;\log_6\left(6^2\right) - \log_6\left(2^2\right)$

. . $=\;\;2\underbrace{\log_6(6)}_{\text{This is 1}} - 2\log_6(2) \;\;=\;\; 2 - 2\log_6(2) \;\;=\; \;2 - 2(0.387) \;\;=\;\;1.226$

4. ## logs

originally postedby Tiger
given logbase6(2)=.387 find logbase6(9)

Gents
Another slight variation

logbase6(9)=2xlog base6(6/2) Result is the same

bjh