Write the following expressions as sum or difference of logarithm… - Vidyadip

Question

Write the following expressions as sum or difference of logarithms:

$\log (\sqrt{x} \sqrt[3]{y})$

✓

Answer

$
\begin{aligned}
\log (\sqrt{x} \sqrt[3]{y})= & \log (\sqrt{x})+\log (\sqrt[3]{y}) \\
& \ldots[\log mn =\log m +\log n ] \\
= & \log x^{\frac{1}{2}}+\log y^{\frac{1}{3}} \\
= & \frac{1}{2} \log x+\frac{1}{3} \log y
\end{aligned}
$
... [ $\left.\log m ^{ n }= nlog m \right]$

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