How do you solve #3 + 2 ln x = 10#?

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Answer 1 · 2015-08-12T23:46:12

#color(red)( x=e^(7/2))#

#3+2lnx=10#

Subtract #3# from each side.

#2lnx=7#

Divide each side by #2#.

#lnx=7/2#

Convert the logarithmic equation to an exponential equation.

#e^lnx = e^(7/2)#

Remember that #e^lnx =x#, so

#x=e^(7/2)#

Check:

#3+2lnx=10#

If #x= e^(7/2)#,

#3+2lne^(7/2)=10#

#3+2(7/2)=10#

#3+7=10#

#10=10#

#x=e^(7/2)# is a solution.