Stationarity in presence of an outlier I am working on a bimonthly data where I have customer the customer's sales amount. I tried to plot the original series in python and the plot
import matplotlib.pyplot as plt

Cust_bimonthly_Data['Customer_Sales'].plot(figsize=(12, 8))
plt.title('Cust Bimonthly Daily')
plt.show()

I tried to plot the above time series in Python and it looks like this


In order to remove this big peak in my data which was an outlier I did log(x+1) transformation on my data i.e. increased all the values to 1 and then did a log transformation
Cust_bimonthly_Data['new_Customer_Sales'] = Cust_bimonthly_Data['new_Customer_Sales']+1
taking the log so as to remove the outliers
Cust_bimonthly_Data['log_cust_sales']=np.log(Cust_bimonthly_Data['new_Customer_Sales'])
**the log transformed series looks like this **

In order to check if my log transformed data is stationary or not I did a ADF test and this is what my results look like
Dickey Fuller test to check if the series transformed series is stationary or not
from statsmodels.tsa.stattools import adfuller
Cust_bimonthly_Data_test= Cust_bimonthly_Data_drop.iloc[:,0].values
result = adfuller(Cust_bimonthly_Data_test)

(-4.8014847417664424,
5.4031369234729222e-05,
0,
63,
{'1%': -3.5386953618719676,
'10%': -2.591896782564878,
'5%': -2.9086446751210775},
150.10425215395222)
question?
Since this test is rejecting the null hypothesis that my series is not stationary , should I still go ahead and perform the decomposition and differencing part. I mean will all those things would still be required since I can see the test tells me that my series is now stationary
 A: One doesn't take logs or any other power transform to deal with anomalous observations like pulses,level shifts,seasonal pulses or local time trends . See When (and why) should you take the log of a distribution (of numbers)? for when to power transform and see http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html for how to deal with anomalies. 
Also the dickey-fuller test requires/assumes that any and all pulses,level shifts,seasonal pulses and local time trends have been incorporated into the model and thus are not present in the current set of residuals.
It looks like you have at least 2 pulses and 2 possible level shifts and possible arima structure. Post your data and I will try and help.
EDITED AFTER RECEIPT OF DATA..
I took your 33 bi-monthly values ( too short to look for seasonal structure ) and used AUTOBOX and obtained the following Actual/Fit and Forecast graph
 . Two pulses and one level shift ...
 The stats are here  and here 
The acf of the residuals is here  suggesting randomness.
(1) IN RESPONSE TO OP'S QUESTION:
the acf of the original series does not suggest non-stationarity  because the level shift obfuscated the variance creating a downwards bias to the acf. Non-stationarity was detected by detecting the presence of a level shift via exploratory data analysy suggesting the need (mandatory) to introduce a level/step shift EXOGENOUS series as the remedy for the non-stationarity . 
A: Perhaps one could assume that data is generated by the linear combination of two processes, one producing seasonality plus perhaps trend and other which incorporates unit impulses to the level of series by certain probability. 
As IrishStat mentioned your complete model must be able to handle that. 
Of course you could use Autobox which David Reilly has created....
