SOLUTION: Could you please help me with this problem Solve for x Ln ( 5-x)=12

Question 27874: Could you please help me with this problem
Solve for x
Ln ( 5-x)=12

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
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
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