Question 27874
Solve for x 
Ln ( 5-x)=12
By  definition  the logarithm of a number to a given base 
is the power to which the base has to be raised to give the number
logb(N) = p   by  definition is     N= (b)^p
In the problem N=(5-x), b= e, the Naperian base and p =12
Therefore  Loge(5-x) = 12
(5-x)= e^12
5-e^12 = x 
Answer:   x = ( 5-e^12 )
Verification: 
log(5-x) = log[5-( 5-e^12 )] 
= log[5-5+e^12] 
= log(0+e^12) 
= log(e^12) 
=12(loge) 
= 12X1  (as loge to the same base e is 1)
=12 which is correct

Note: If the base is the common base 10, then we have
Loge(5-x) = 12 giving
(5-x)= 10^12
5-10^12 = x 
Answer:   x = ( 5-10^12 )
Verification: 
log(5-x) = log[5-( 5-10^12 )] 
= log[5-5+10^12] 
= log(0+10^12) 
= log(10^12) 
=12(log10) 
= 12X1  (as log10 to the same base 10 is 1)
=12 which is correct