Question

log3(x+1)=2+log3(x-3)

Answer 1

first isolate the log terms on one side of the equation
then apply laws of logs and convert to exponential form

Answer 2

log3(x+1)=2+log3(x-3)
log3(x +1) - log3(x-3) = 2

log3[ (x+1)(x-3)] = 2

now convert to exponential form

Answer 3

log3(x-2)=2?

Answer 4

no

use the definition of loge

i loga x = b then
a^b = x

Answer 5

in your problem a=3 , b = 2 and x = (x+!)/(x-3)