Final answer:
To solve the equation 7⁵t - 3 = 10³t - 2, rearrange to get 0 on one side and use the quadratic formula to solve for t. The solutions are t = 8 or t = -18.
Step-by-step explanation:
To solve the equation 75t - 3 = 103t - 2, we can rearrange the equation to get 0 on one side: 75t - 103t = 1.
Then, we can use the quadratic formula to solve for t.
Rearranging the equation further, we get t² + 10t - 200 = 0.
Using the quadratic formula, t = (-b ± √(b² - 4ac)) / (2a), where a = 1, b = 10, and c = -200. Solving for t, we find two solutions: t = 8 or t = -18.