The discussion revolves around expressing the mathematical expression ##3^{\sqrt{2}}## in terms of natural logarithms, as posed in a calculus textbook. Participants explore various approaches and interpretations of the problem, which falls under the category of mathematical reasoning.
Participants express differing views on how to properly express ##3^{\sqrt{2}}## in terms of natural logarithms, with no consensus reached on a definitive method or solution. The discussion remains unresolved regarding the correct approach.
Participants note that the original question may lack sufficient detail, and there are unresolved assumptions about what constitutes a complete answer in natural logarithm form.
Are you sure?MevsEinstein said:All I know is that ##3^{sqrt{2}} = e^{2*ln{3}}##
Perhaps that form is what they want?MevsEinstein said:but that's not completely in natural logarithm form.
You should correct your mistake, then write ##x=3^{\sqrt{2}}## and transform it via logarithm and exponentiation.MevsEinstein said:Summary:: What the title says
So in my Calculus book, it asked a question in its Transcendental Functions chapter. It wanted me to express ##3^{\sqrt{2}}## in terms of natural logarithms I have no idea how to solve this. All I know is that ##3^{\sqrt{2}} = e^{2\ln{3}}## but that's not completely in natural logarithm form.
The question was to represent ##3^\sqrt{2}## as natural logarithms. ##\sqrt{2} \ln{3}## won't be the answermathman said:Maybe ##ln(3^{\sqrt{2}})=\sqrt{2}ln(3)?##
Again. Set ##x=3^{\sqrt{2}}## and rewrite it as ##x=e^{\ln x}## with appropriate changes on the right.MevsEinstein said:The question was to represent ##3^\sqrt{2}## as natural logarithms. ##\sqrt{2} \ln{3}## won't be the answer
The book didn't have any other examples.Office_Shredder said:I think this question is underspecified. Do you have some other examples with correct solutions so we can try to figure out what they're actually looking for?