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.