Your friend asks you to help him with his snow shoveling business and will pay you 3 pennies for the first job. You agree to help if he triples your payment for each job completed. After 2 shoveling jobs, you will receive 9 pennies, and after 3 shoveling jobs, you will receive 27 pennies. Complete and solve the equation that finds the number of pennies he will pay you after the seventh shoveling job.
Let's say x represents the number of shoveling jobs completed. According to the given information, we can set up the equation:
3 * 3^x = 7
To solve for x, we can take the logarithm of both sides. Assuming base 3:
log₃(3 * 3^x) = log₃(7)
1 + log₃(3^x) = log₃(7)
x * log₃(3) + 1 = log₃(7)
x * 1 + 1 = log₃(7)
x + 1 = log₃(7)
Subtracting 1 from both sides:
x = log₃(7) - 1
Using a calculator, we can find that log₃(7) ≈ 1.7712. Therefore:
x ≈ 1.7712 - 1
x ≈ 0.7712
Since we can't have a fraction of a job, we need to round up to the nearest whole number, which is 1. Thus, after the seventh shoveling job, he will pay you 3 * 3^1 = 3 * 3 = 9 pennies.