How do you expand #ln(x/sqrt(x^6+3))#?

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Answer 1 · 2016-09-04T22:25:22

The expression can be simplified to #lnx - 1/2ln(x^6 + 3)#

Start by applying the rule #log_a(n/m) = log_a(n) - log_a(m)#.

#=>ln(x) - ln(sqrt(x^6 + 3))#

Write the #√# in exponential form.

#=> lnx - ln(x^6 + 3)^(1/2)#

Now, use the rule #log(a^n) = nloga#.

#=>lnx - 1/2ln(x^6 + 3)#

This is as far as we can go.

Hopefully this helps!