How do I solve logarithms?

Question

ln lxl =1

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Answer 1 · 2018-04-20T12:30:06

Please see below.

Here,

#ln |x|=1=>log_e|x|=1#

We know that,

#log_ex=y<=>x=e^y,where, x > 0#

#:.log_e|x|=1=>|x|=e^1#

#i.e. |x|=e=>x=+-e#

Note:

#"ln (x) is undefined when"# # x<=0"#

So, #ln|x|=ln|+-e|=ln e=1#

Answer 2 · 2018-04-20T12:30:28

#x=+-e#

We use the definition:

# log_b x = y iff b^y = x#

So for the given expression:

# ln|x|=1 iff e^1 = |x| #

# :. |x| = e => x =+-e#