Question

logarithms question​

Answer 1

Answer

$\sf\implies \frac{2}{3}log(x) + log(y) - \frac{2}{5}log(z)$

Solution

We will use the following properties

★$\sf\sqrt[m]{x^n} = x^{\frac{n}{m}}$

★log(mn) = log(m) + log(n)

★$\sf log(\frac{m}{n}) = log(m) - log(n)$

So,

$\sf log(\frac{\sqrt[3]{x^2} \times y}{\sqrt[5]{z^2}})$

$\sf\implies log(\frac{x^{\frac{2}{3}}\times y}{z^{\frac{2}{5}}})$

$\sf\implies log(x^{\frac{2}{3}}) + log(y) - log(z^{\frac{2}{5}})$

Now using

$\sf log_a(m^p) = plog_a(m)$, we can write it as

$\sf\implies \frac{2}{3}log(x) + log(y) - \frac{2}{5}log(z)$

Answer 2

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The Entire Solution Is In The Attachment.

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