Question 611672
<font face="Times New Roman" size="+2">


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\,\cdot\,\log_4(6)\ -\ \log_4(8)\ =\ \log_4(x)] 


Use:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n)\ =\ n\log_b(x)]


to write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_4(6^3)\ -\ \log_4(8)\ =\ \log_4(x)]


Use: "The difference of the logs is the log of the quotient" to write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_4( \frac{6^3}{8} )\ =\ \log_4(x)]


Use:


*[tex \LARGE \ \ \ \ \ \ \ \ \log_b(x)\ =\ \log_b(y)\ \ \Leftrightarrow\ \ x\ =\ y]


To write:


*[tex \LARGE \ \ \ \ \ \ \ \ x\ =\ \frac{6^3}{8}]


Just do the arithmetic.  Hint *[tex \LARGE 6^3 = 36\,\cdot\,6] and 36 is divisible by 4 while 6 is divisible by 2, 4 and 2 being the factors of the denominator.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>