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Levart [38]
3 years ago
10

Expand a logarithmic expression

Mathematics
2 answers:
ivanzaharov [21]3 years ago
8 0

The logarithmic expression is

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

To expand the expression we have to use some properties of logarithm.

We know that log(m/n) = log (m) - log(n)

By using this property we can write,

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

Square root means to the power 1/2, so for \sqrt{z^5}, we can write z^(5/2).

log(z^(5/2)) - log(x^3y)

Now we have to use another property of logarithm.

We know that, log(mn) = log(m) + log(n)

So we will use this property to log(x^3y)

log(z^(5/2)) - log(x^3y)

log(z^(5/2)) - (log(x^3) + log(y))

log(z^(5/2)) - log(x^3) - log(y)

Now we have to use another property of logarithm.

We know that, log(a^m) = m log(a)

By using this property we can write,

(5/2)log(z) - 3log(x) - log(y)

This is the required aswer here.

irinina [24]3 years ago
7 0

we have logarthmic division function .

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

we know that log(a/b)=log a-log b

so the given function will be log(\sqrt{z^5} )-log(x^3y)=\frac{5}{2} logz-(3logx+logy)

we know that if a exponent in log is bought down it will be multiplied with log

so we got square root of z^5 and x^3 as 5/2 and 3 .

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