July 26th, 2016, 02:43 PM  #1 
Newbie Joined: Jun 2016 From: New York Posts: 14 Thanks: 0 Math Focus: Calculus and Algebra  How does one do dis???
A and B please I don't get how they're supposed to be done???

July 26th, 2016, 03:16 PM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,596 Thanks: 620 Math Focus: Wibbly wobbly timeywimey stuff. 
Can you write it out or at least make sure the image is large enough to read (and right side up?) Dan 
July 26th, 2016, 03:32 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,973 Thanks: 2296 Math Focus: Mainly analysis and algebra 
I would start a) by determining the value of each of the logarithms.

July 26th, 2016, 04:15 PM  #4 
Newbie Joined: Jun 2016 From: New York Posts: 14 Thanks: 0 Math Focus: Calculus and Algebra 
Log base 2 of 2 times Log Base 2 of 4 times Log Base 2 of 8 ••• log base 2 of 2^10 is a find the exact value and B is Log base 2 of 4 times log base 4 of 6 times log base 6 of 8 ••• log base 14 of 16 find the exact value 
July 26th, 2016, 08:41 PM  #5 
Senior Member Joined: May 2016 From: USA Posts: 803 Thanks: 320 
$\displaystyle \prod_{i=1}^{10} log_2(2^i) = \prod_{i=1}^{10} \{ilog_2(2)\} = \prod_{i=1}^{10} (i * 1) = \prod_{i=1}^{10} i = what?$ The pi means to multiply as many times as indicated. There is nothing hard about this problem, but it is cumbersome without knowing a convenient notation. 
July 27th, 2016, 03:17 AM  #6 
Newbie Joined: Jun 2016 From: New York Posts: 14 Thanks: 0 Math Focus: Calculus and Algebra 
Now what about the productmation (I'm not even sure that's what you call it, of B when the log base changes?

July 27th, 2016, 04:16 AM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319 
$\log_2(4) \cdot \log_4(6) \cdot \log_6(8 ) \cdot ... \cdot \log_{14}(16)$ Change of base ... let all the logs in the next expression be base 2 $\dfrac{\log(4)}{\log(2)} \cdot \dfrac{\log(6)}{\log(4)} \cdot \dfrac{\log(8 )}{\log(6)} \cdot \, ... \, \cdot \dfrac{\log(16)}{\log(14)}$ this will simplify to $4$ ... do you see why? 
July 27th, 2016, 07:11 AM  #8 
Senior Member Joined: May 2016 From: USA Posts: 803 Thanks: 320 
This is skeeter's answer in the pi notation. Note that $log_2(4) = \dfrac{log_2(4)}{1} = \dfrac{log_2(4)}{log_2(2)}.$ $\displaystyle \prod_{i=1}^7 log_{2i}\{2(i+1)\} = \prod_{i=1}^7 \dfrac{log_2\{2(i+1)\}}{log_2(2i)}= \dfrac{\displaystyle \prod_{i=1}^7 log_2 \{2(i + 1)\}}{\displaystyle \prod_{i=1}^7 log_{2} (2i)} =$ $\dfrac{\displaystyle \prod_{i=2}^8log_2(2i)}{\displaystyle \prod_{i=1}^7 log_2(2i)} = \dfrac{log_2(8 * 2) * \cancel{\displaystyle \prod_{i=2}^7 log_2(2i)}}{log_2(2 * 1) * \cancel{\displaystyle \prod_{i=2}^7 log_2(2i)}} = \dfrac{log_2(16)}{log_2(2)} = 4.$ In this case, skeeter's notation is more intuitive. 
July 27th, 2016, 06:03 PM  #9  
Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319  Quote:
 