Question

Express the following in single logorithemic form 4 log a+2loga-2logc

Answer 1

To express the following in single logorithemic form 4 log a+2loga-2logc

We know that
$n log(a) = log( {a}^{n} )$
So

$4 log(a) = log( {a}^{4} ) \\ \\ 2 log(a) = log( {a}^{2} ) \\ \\ 2 log(c) = log( {c}^{2} )$
we also know that

$log(a) + log(b) + log(c) = log(abc)$
So

$4 log(a) + 2 log(a) + 2 log(c) = log( {a}^{4} {a}^{2} {c}^{2} ) \\ \\ = log( {a}^{6} {c}^{2} )$