![\"\"](\"/userfiles/image/steps_images/step1.JPG\")
Properties of Natural Logarithmic Function:
\The domain of the natural logarithmic function is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=bf7c434a0db5722e5061b38f166a169f.png\")
and the range is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a4382225c325271dfaf441344e5581d2.png\")
.
The function is continuous, increasing, and one-to-one.
\The graph is concave downward.
\In addition , if ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=52257f1605fb2b790995dd69987af2c6.png\")
and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=b72515eceac9b0f2954ec68f910b8672.png\")
are positive numbers and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=9d9525296c7189f71cd1cbb29d5a4593.png\")
is rational, then
(a) ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=55e37a29b51f2531a3bafb57f788a630.png\")
.
(b) ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=5f2398dad4d706943a90d27aac9251d2.png\")
.
(c) ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=836a6acfe932580b70c04f825767c2fb.png\")
.
(d) ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=d09681b67295d94d2d8ecb6f4242f0bc.png\")
.
![\"\"](\"/userfiles/image/steps_images/solution.JPG\")
The domain of the natural logarithmic function is and the range is .
The function is continuous, increasing, and one-to-one.
\The graph is concave downward.
\In addition , if and are positive numbers and is rational, then
(a) .
(b) .
(c) .
(d) .