Write the following expressions as a single logarithm. 5 x+7 y- z - Vidyadip

Question

Write the following expressions as a single logarithm.
$5 \log x+7 \log y-\log z$

✓

Answer

$5 \log x+7 \log y-\log z$
$=\log \left(x^5\right)+\log \left(y^7\right)-\log z$
$\ldots\left[n \log m=\log m^n\right]$
$=\log \left(x^5 y^7\right)-\log \mathrm{z}$
$\ldots[\log m+\log n=\log m n]$
$=\log \left(\frac{x^5 y^7}{z}\right)$
$\ldots\left[\log m-\log n=\log \frac{m}{n}\right]$

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