Solve for x:
Log base 2 of ( x+1) = Log base ( x+1) of 2
In general, log_a(b) = 1/log_b(a)
so, you have
log_2(x+1) = 1/(1/log_2(x+1))
(log_2(x+1))^2 = 1
log_2(x+1) = ±1
x+1 = 2 or 1/2
x = 1 or -1/2
check:
log_2(2) = log_2(2) = 1
log_2(1/2) = log_1/2(2) = -1