The points (5, -2 log8(t)) and (-4 log8(t), 5) lie on a line parallel to y = 7x + 2024.
Determine all possible values of t.
Solution:
The answer is t = 1/16.
Since the two given points lie on a line parallel to y = 7x + 2024, the slope of the line containing the two points must be equal to 7. Use the formula for slope to set up the following equation:
Then 5 + 2 log8(t) = -28 log8(t) - 35
30 log8(t) = -40
log8(t) = -4/3
8 -4/3 = t
Another way to solve the problem is to substitute the coordinates of the two points into the general form of a line parallel to y = 7x + 2024.
The equation of the line is y = mx + 2024.
After substituting the two points, you obtain 2 equations with two variables:
-2 log8(t) = m (5) + 2024
5 = m ( -4 log8(t)) + 2024
Now solve the two equations simultaneously.
Correctly solved by:
| 1. Kamal Lohia |
Holy Angel School, Hisar, Haryana, India |
| 2. K. Sengupta | Calcutta, India |
| 3. Dr. Hari Kishan |
D.N. College, Meerut, Uttar Pradesh, India |
| 4. Davit Banana | Istanbul, Turkey |
| 5. Kelly Stubblefield | Mobile, Alabama, USA |