Explain the differences between solving log_3⁡〖(x-1)〗=4 and log_3⁡〖(x-1)〗=log_3⁡(4)

Question

Writing in mathematics

Answer 1

For log₃(x-1)=4 we need to get rid of the log so that we're dealing with ordinary numbers. To do this:

3^log₃(x-1)=3⁴ is also true, and this can be solved:

x-1=81, so x=82.

log₃(x-1)=log₃(4) is easier to solve because we only need to consider the arguments of the logs, which are both to the same base:

x-1=4, x=5.