How do you solve #e^(ln(sinx))=1# in the interval [0,360]?

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Answer 1 · 2016-11-05T03:12:14

#x= 90˚#.

Take the natural logarithm of both sides.

#ln(e^(ln(sinx))) = ln1#

Simplify using the rule #lna^n = nlna#.

#ln(sinx)(lne) = 0#

Apply the identity #ln(e) = 1#.

#ln(sinx) = 0#

#sinx = e^0#

#sinx = 1#

#x = 90˚#

Hopefully this helps!