Explain the differences between solving these two equations:

Question

Brake down the steps.

log3(x - 1) = 4 and log3(x - 1) = log34 )

Answer 1

1. log3(x - 1) = 4.

x - 1 = 3^4,
x = 3^4 + 1 = 81 + 1 = 82.

2. log3(x - 1) = log34.

log3(x - 1) = 1.5315,
x - 1 = 3^1.5315,
x = 3^1.5315 + 1 = 5.379 + 1 = 6.379.

Each problem required the use and understanding 0f logs. So they were basically the same.

Answer 2

2. log3(x - 1) = log3(4).

If two numbers have equal logs, they are equal:
x-1 = 4,
x = 4 + 1 = 5.