How do you find the exact value of #lnroot4(e^3)#?

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Answer 1 · 2017-01-04T23:13:19

#3/4#

Use #root(n)(a^m) = a^(m/n)#.

#=ln (e^(3/4))#

Use the rule #lna^n = nlna#:

#=3/4lne#

Since #y = lnx# and #y = e^x# are inverses, their product will be #1#.

#=3/4#

Hopefully this helps!