Difference between revisions of "1950 AHSME Problems/Problem 25"
(Created page with "== Solution == <math> \log_{5}\frac{(125)(625)}{25} </math> can be simplified to <math> \log_{5}\ (125)(25) </math> since <math>25^2 = 625</math>. <math>125 = 5^3</math> and <ma...") |
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| + | ==Problem== | ||
| + | The value of <math> \log_{5}\frac{(125)(625)}{25} </math> is equal to: | ||
| + | |||
| + | <math> \textbf{(A)}\ 725\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 3125\qquad\textbf{(D)}\ 5\qquad\textbf{(E)}\ \text{None of these} </math> | ||
| + | |||
== Solution == | == Solution == | ||
<math> \log_{5}\frac{(125)(625)}{25} </math> can be simplified to <math> \log_{5}\ (125)(25) </math> since <math>25^2 = 625</math>. <math>125 = 5^3</math> and <math>5^2 = 25</math> so <math> \log_{5}\ 5^5 </math> would be the simplest form. In <math> \log_{5}\ 5^5 </math>, <math>5^x = 5^5</math>. Therefore, <math>x = 5</math> and the answer is <math>\boxed{\mathrm{(D)}\ 5}</math> | <math> \log_{5}\frac{(125)(625)}{25} </math> can be simplified to <math> \log_{5}\ (125)(25) </math> since <math>25^2 = 625</math>. <math>125 = 5^3</math> and <math>5^2 = 25</math> so <math> \log_{5}\ 5^5 </math> would be the simplest form. In <math> \log_{5}\ 5^5 </math>, <math>5^x = 5^5</math>. Therefore, <math>x = 5</math> and the answer is <math>\boxed{\mathrm{(D)}\ 5}</math> | ||
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| + | {{AHSME box|year=1950|num-b=22|num-a=24}} | ||
Revision as of 11:11, 29 December 2011
Problem
The value of 
is equal to:
Solution
can be simplified to 
since 
. 
and 
so 
would be the simplest form. In , 
. Therefore, 
and the answer is 
| 1950 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
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| All AHSME Problems and Solutions | ||
