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sp2606 [1]
2 years ago
6

Expand a logarithmic expression.

Mathematics
1 answer:
Korolek [52]2 years ago
4 0

we are given

log(z^3\sqrt{x^5y} )

step-1: Firstly , we will expand log terms by using property

log(a*b)=log(a)+log(b)

log(z^3)+log(\sqrt{x^5y} )

step-2: Now, we can bring exponent in front

log(a^n)=n*log(a)

=log(z^3)+log(x^5y)^{\frac{1}{2}}

=3log(z)+\frac{1}{2}log(x^5y)

step-3: we can again expand second term

=3log(z)+\frac{1}{2}(log(x^5)+log(y))

=3log(z)+\frac{1}{2}(5log(x)+log(y))

so, we will get

=3log(z)+\frac{1}{2}(5log(x)+log(y))...............Answer

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