How do you solve #lnsqrt(x) = 3#?

1 Answer
Patrick H.
Jun 23, 2018

Rearrange the expression so its shown as an exponential function.

Explanation:

You probably know that #ln#, or "natural logarithm" for short, has #e# as its base. You may also know that a logarithm #log_a b=x# can be rewritten as #a^x=b#. Let's rewrite the expression using these:

#log_e sqrt(x)=3#
#e^3=sqrt(x)#

Next, let's square each side to get our answer:

#(e^3)^2=(sqrt(x))^2#
#e^6=x~~403.43#

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