how to compare two columns in dataframe and update a column based on matching fields

I Have two dataframe as shown below

|a|b|c|
|1|2| |
|4|5| |
|7|8| |

2nd dataframe is

|a_1|b_1|
|1  |5  |
|4  |2  |
|7  |8  | 

I want to compare two common columns (a,a_1) and update the 3rd column in my 1st dataframe Expected output is shown below

    |a|b|c|
    |1|2|5|
    |4|5|2|
    |7|8|8|

Is there a code to match common column and populate 3rd column kindly help on this regard.

>Solution :

import pandas as pd

d1={
    "a":(1,4,7),
    "b":(2,5,8),
}

d2={
    "a_1": (1, 4, 7),
    "b_1": (5, 2, 8)
}

df1=pd.DataFrame(d1)
df2=pd.DataFrame(d2)

c_col_list=[]

# Iterate through each entry in a and compare it to a_1
for i in range(len(df1["a"])):
    if df1["a"][i] == df2["a_1"][i]:
        # If they match, append the value to our list
        c_col_list.append(df2["b_1"][i])

# add the generated list as your c column
df1["c"]=c_col_list