How do you solve #5\ln ( 5x + 1) - 17= - 27#?

1 Answer
Fleur
Oct 19, 2017

#x = 1/(5e^2) - 1/5#

Explanation:

#5 ln (5x + 1) - 17 = -27#

#5 ln(5x+1) = -10#

#ln(5x+1) = -10/5#

#ln(5x+1) = -2#

To eliminate #ln# from the equation, we can use the property #e^(ln x) = x#.

#e^(ln(5x+1)) = e^(-2)#

#5x + 1 = e^(-2)#

#5x = e^(-2) - 1#

#x = (e^(-2) - 1)/5#

#x = e^(-2)/5 - 1/5#

#x = 1/(5e^2) - 1/5#

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