Difference between revisions of "1977 AHSME Problems/Problem 18"
(Created page with "== Problem 18 == If <math>y=(\log_23)(\log_34)\cdots(\log_n[n+1])\cdots(\log_{31}32)</math> then <math>\textbf{(A) }4<y<5\qquad \textbf{(B) }y=5\qquad \textbf{(C) }5<y<6\qq...") |
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| − | Note that <math>\ | + | Note that <math>\log_{a}b = \dfrac{\log{b}}{\log{a}}</math>. Then <math>y=(\dfrac{\log3}{\log2})(\dfrac{\log4}{\log3})\cdots(\dfrac{\log32}{\log31}) = \dfrac{\log32}{\log2} = \log_232 = \boxed{\text{(B) }y=5}</math>. |
Latest revision as of 12:05, 22 November 2016
Problem 18
If ![$y=(\log_23)(\log_34)\cdots(\log_n[n+1])\cdots(\log_{31}32)$](http://latex.artofproblemsolving.com/c/5/b/c5ba4fa4829cb4897af6dbab5fe894d0780427b5.png)
then
Solution
Solution by e_power_pi_times_i
Note that 
. Then 
.
