What is the solution to the equation #e^(5-3x)=10#?

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Answer 1 · 2018-04-22T02:27:47

#x=(5-ln10)/3#

Apply the natural logarithm to both sides:

#ln(e^(5-3x))=ln10#

Recalling the exponent property for logarithms, which tells us that #ln(a^b)=blna,# we rewrite as

#(5-3x)lne=ln10#

#lne=1,# so we get

#5-3x=ln10#

Solve for #x:#

#3x=5-ln10#

#x=(5-ln10)/3#