What is the logarithmic form of the equation?

The answer is as follows:

3^x=14
=>
xlog(10)3=log(10)14
or
xlog(3)3=log(3)14
=>
x=log(3)14

take logs to base '10' on both sides 
Hence 
log(10)3^x = log(10)14 
By the rules of logs , 'xx' can be moved to a coefficient. 
xlog(10)3 = log(10)14 

You can use base 'e' . shown as 'ln' on the calculator. 
Hence 
xln3 = ln14 

NB DO NOT mix log bases.  There is an equation to convert log bases. 

3^(x) = 14

Ln[3^(x)] = Ln(14)

x.Ln(3) = Ln(14)

x = Ln(14) / Ln(3)

x = Log[3](14)

Log[3](14) = x → where 3 is te base

Take the log of both sides
x log3 = log14
x = log14/log3

Remembering the logarithmic change of base rule
x = log₃ 14 

log_3 14 = x
  
If you commit to remembering 
log_10  100 = 2       (or just log 100 = 2)
10² = 100 
   
then you can swap between forms by comparing.