Question

Write $4\log 4+2\log 5-\log 15$ as a single logarithm.

Answer 1

$4\log 4+2\log 5-\log 15$

$\Rightarrow$ $\log 256+\log 25-\log 15$

$\Rightarrow$ $\log \left(\frac{256\times 25}{15}\right)$

$\Rightarrow$ $\log \left(\frac{6400}{15}\right)$

$\Rightarrow$ $\log \left(\frac{1280}{3}\right)$

$\therefore 4\log 4+2\log 5-\log 15=\log \left(\frac{1280}{3}\right)$