how would ya go about solving this equation:

Question

how would ya go about solving this equation:

log₃(16x+1) = log₃(x-4) + 4

thanks

Answer 1

An alternative way to solve the problem is by using properties of Logs.

1. log₃(16x + 1) = log₃(x - 4) + 4
2. log₃(16x + 1) - log₃(x - 4) = 4 Put the logs on what side since they have the same base
3. log₃((16x + 1) / (x -4)) = 4 Combined the logs into one log using division property
4. (16x + 1) / (x - 4) = 3⁴ Put 3 as a base for both sides to cancel out the logs
5. 6x + 1 = 81x - 324, Solve for x
6. Solving for x you get x = 5

Answer 2

log₃(16x + 1) = log₃(x - 4) + 4; because 4 = log₃81, we have log₃(16x + 1) = log₃[81(x - 4)]; or 16x + 1 = 81x - 324, 65x = 325, x = 5