Difference between revisions of "1950 AHSME Problems/Problem 25"
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− | == | + | == Problem == |
+ | The value of <math> \log_{5}\frac{(125)(625)}{25} </math> is equal to: | ||
− | <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> \textbf{(A)}\ 725\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 3125\qquad\textbf{(D)}\ 5\qquad\textbf{(E)}\ \text{None of these} </math> |
+ | |||
+ | == Solutions == | ||
+ | === Solution 1 === | ||
+ | <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>. | ||
+ | |||
+ | === Solution 2 === | ||
+ | <math> \log_{5}\frac{(125)(625)}{25} </math> can be also represented as <math> \log_{5}\frac{(5^3)(5^4)}{5^2}= \log_{5}\frac{(5^7)}{5^2}= \log_{5} 5^5 </math> which can be solved to get <math>\boxed{\mathrm{(D)}\ 5}</math>. | ||
+ | |||
+ | == See Also == | ||
+ | {{AHSME 50p box|year=1950|num-b=24|num-a=26}} | ||
+ | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 23:58, 11 October 2020
Contents
[hide]Problem
The value of is equal to:
Solutions
Solution 1
can be simplified to since . and so would be the simplest form. In , . Therefore, and the answer is .
Solution 2
can be also represented as which can be solved to get .
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
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