How do you write #log_14 196=2# in exponential form?

Suppose you had #log_ax=y#

They would call this log to base #a#

Then it means: #a^y=x# .............................Equation(1)

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Note that #log_a(a)=1#

So:
#log_2(2)=1" "->" "2^1=2#
#log_10(10)=1" "->" "10^1=10#
#log_e(e)=1" "->" "e^1=e#

#Log_e# is a special one case.

You normally see this written as #ln#

So you could have #ln(x)# sometimes you see it as #exp(x)#

The last one is quite often used in computer software and in higher maths.

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Note that #log_10(1)=0# as is any #log_x(1)=0#

Look at Equation(1) and you will observe that

as in #log_ax=y" "->" "a^y=x#

#" "log_10(1)=0" "->" "10^0=1#

Any value (apart from 0) raised to the power of 0 has the value 1

Consider: #x^z/x^z =1# this is the same as #x^(z-z) =x^0=1#

Changing from log from to index form can be done by purely following the definition.

#log_a b = c " " rArr " a^c = b#

Remember:
"The base stays the base and the other two change around"

#log_14 196 = 2" " rArr " " 14^2 = 196#