How do you solve #119/(e^(6x)-14)=7#?

1 Answer
Jan 18, 2017

#x=1/6ln31#

Explanation:

#frac{119}{e^(6x)-14}=7#

Multiply each side by #(e^(6x)-14):#
#119=7(e^(6x)-14)#

Divide each side by 7:
#17=e^(6x)-14#

Add 14 to each side:
#31=e^(6x)#

Take the natural log of each side:
#ln(31)=ln(e^(6x))#

#6x=ln31#

Divide each side by 6:
#x=1/6ln31#

Check answer by confirming #e^(6x)-14 cancel=0# (Make sure denominator of original equation is not zero)
#e^(6x)=14#
#6x=ln14#
#x=1/6ln14#
#1/6ln31cancel=ln14#