SOLUTION: how do you simplify e^ln(sin(x)) and e^3ln(x)

Algebra ->  Sequences-and-series -> SOLUTION: how do you simplify e^ln(sin(x)) and e^3ln(x)      Log On


   

Question 985937: how do you simplify e^ln(sin(x)) and e^3ln(x)
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
e%5E%28ln%28sin%28x%29%29%29 = sin%28x%29       (provided  sin(x) > 0).

e%5E%283ln%28x%29%29 = x%5E3                (provided  x > 0).

It is the basic property of a logarithm:   a%5Elog%28a%2Cx%29 = x   for any  a > 0,  a=/=1  and  x > 0.

See the lesson  WHAT IS the logarithm  in this site.