Difference between revisions of "1957 AHSME Problems/Problem 5"
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+ | == Problem 5== | ||
+ | |||
+ | Through the use of theorems on logarithms | ||
+ | <cmath>\log{\frac{a}{b}} + \log{\frac{b}{c}} + \log{\frac{c}{d}} - \log{\frac{ay}{dx}} </cmath> | ||
+ | can be reduced to: | ||
+ | |||
+ | <math>\textbf{(A)}\ \log{\frac{y}{x}}\qquad | ||
+ | \textbf{(B)}\ \log{\frac{x}{y}}\qquad | ||
+ | \textbf{(C)}\ 1\qquad \\ | ||
+ | \textbf{(D)}\ 140x-24x^2+x^3\qquad | ||
+ | \textbf{(E)}\ \text{none of these} </math> | ||
+ | |||
+ | ==Solution== | ||
Using the properties <math>\log(x)+\log(y)=\log(xy)</math> and <math>\log(x)-\log(y)=\log(x/y)</math>, we have | Using the properties <math>\log(x)+\log(y)=\log(xy)</math> and <math>\log(x)-\log(y)=\log(x/y)</math>, we have | ||
<cmath>\begin{align*} | <cmath>\begin{align*} |
Latest revision as of 00:20, 4 January 2019
Problem 5
Through the use of theorems on logarithms can be reduced to:
Solution
Using the properties and , we have so the answer is