Difference between revisions of "1975 AHSME Problems/Problem 19"
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Which positive numbers <math>x</math> satisfy the equation <math>(\log_3x)(\log_x5)=\log_35</math>? | Which positive numbers <math>x</math> satisfy the equation <math>(\log_3x)(\log_x5)=\log_35</math>? |
Latest revision as of 17:21, 19 January 2021
Problem
Which positive numbers satisfy the equation ?
Solution
By the change-of-base formula, we can simplify the left side of the equation: .
We see that this in fact simplifies to , which will always equal the right side of the equation, since they are the same exact expressions.
But we have to be careful because . Plugging in , the left side would equal , and definitely does not equal .
Besides , can take on any positive value, and the equation would work. Therefore, the answer is ~jiang147369
See Also
1975 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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All AHSME Problems and Solutions |
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