1996 AHSME Problems/Problem 8
Contents
Problem
If and , then
Solution
We want to find , so our strategy is to eliminate .
The first equation gives .
The second equation gives
Setting those two equal gives
Cross-multiplying and dividing by gives .
We know that , so we can divide out from both sides (which is legal since ), and we get:
, which is option .
Solution 2
Take corresponding logs and split up each equation to obtain:
Then subtract the log from each side to isolate r:
Then set equalities and solve for k:
After solving we find that . Plugging into either of the equations and solving (easiest with equation 1) we find that
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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