Use the same-derivative argument, as was done to

Alessandra Carrillo 2022-04-11 Answered
Use the same-derivative argument, as was done to prove the Productand Power Rules for logarithms, to prove the Quotient Ruleproperty.
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Answers (1)

Jax Burns
Answered 2022-04-12 Author has 13 answers

The objective is to prove the property ln(bx)=lnblnx
Differential ln(bx)
d dx (ln(bx))=1dxd dx (bx)
=xb(bx2)
=1x
Integrate both the sides of the equation with respect to x as,
lnbx=(ln1)+c
c=lnb
Substitute c=lnb in the equation ln(bx)=(lnx)+c as,
lnbx=(lnx)+lnb
ln(bx)=lnblnx
Hence, Proved

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