SOLUTION: Find the value of log2(3) log3(4) log4(5) … log1023(1024). (Hint:Use change of base formula)

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Question 1089581: Find the value of log2(3) log3(4) log4(5) … log1023(1024). (Hint:Use change of base formula)
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+log%282%2C%283%29%29log%283%2C%284%29%29log%284%2C%285%29%29 … log%281023%2C%281024%29%29+
Using 'log' to denote log base 10 (i.e. the traditional log function):
= … *
Notice how log(3) cancels with log(3) of the 2nd factor, and then log(4) cancels, etc. leaving us with
=

Answer by ikleyn(52852) About Me  (Show Source):
You can put this solution on YOUR website!
.
   = 


         Use the base change formula  log%28a%2C%28b%29%29 = log%28b%29%2Flog%28a%29 to get


=  = (cancel all appropriate factors) = 

= log%281024%29%2Flog%282%29 = (use the base change formula again to get) = log%282%2C%281024%29%29 = 10.

Solved.


On logarithms and their properties, see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Solving logarithmic equations
    - Using logarithms to solve real world problems
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".