1974 AHSME Problems/Problem 18: Difference between revisions
Created page with "==Problem== If <math> \log_8{3}=p </math> and <math> \log_3{5}=q </math>, then, in terms of <math> p </math> and <math> q </math>, <math> \log_{10}{5} </math> equals <math> \mat..." |
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==See Also== | ==See Also== | ||
{{AHSME box|year=1974|num-b=17|num-a=19}} | {{AHSME box|year=1974|num-b=17|num-a=19}} | ||
[[Category:Introductory Algebra Problems]] | |||
{{MAA Notice}} | |||
Latest revision as of 11:43, 5 July 2013
Problem
If 
and 
, then, in terms of 
and 
, 
equals
Solution
Notice that 
, so it would probably be easier to work in base 
. From change of base, 
. We're given that 
, so now we just need to find 
.
We have 
, so 
. Also, 
. Therefore, 
.
See Also
| 1974 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America. 
