Simplify $5lnx +21lnx^3-3lnx^3+lnx^(1/2)$ ?

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Answer 1 · 2017-03-03T13:06:43

$5lnx +21lnx^3-3lnx^3+lnx^(1/2)=119/2lnx$

We can use the identities $lna+lnb-lnc=ln((ab)/c)$ and $lna^b=blna$ .

Hence,

$5lnx +21lnx^3-3lnx^3+lnx^(1/2)$

= $5lnx +21xx3lnx-3xx3lnx+1/2lnx$

= $5lnx +63lnx-9lnx+1/2lnx$

= $lnx(5+63-9+1/2)$

= $lnx(59+1/2)$

= $119/2lnx$

Simplify 5lnx +21lnx^3-3lnx^3+lnx^(1/2)5lnx +21lnx^3-3lnx^3+lnx^(1/2)?