Question

express $\log q^3-\log 64+\frac{1}{2}\log 16$ as a single logarithm.

Answer 1

$log{q}^3-log64+\frac{1}{2}log16$

$\Rightarrow log(\frac{q^3}{64}.\sqrt{16})$

$\{loga-logb=log(\frac{a}{b})$

$loga+logb=log\left(ab\right)\}$

$=log\left(\frac{q^3.4}{64}\right)$

$=log\left(\frac{q^3}{16}\right)$

$=\left(log\right[\frac{q^3}{2^4}\left]\right)$