Question 167293
Express as a single logarithm
{{{  1/2 }}}log{{{ a }}}   b + 3 log {{{ a }}} c -  5 log {{{ a }}} d -  10  log {{{ a }}} f
Since all terms are to the same base (a), assume base a.
1/2log(b) + 3 log(c) -  5 log(d) -  10log(f)
= {{{log(sqrt(b)) + log(c^3) +log(d^-5) + log(f^(-10))}}}
= {{{log(sqrt(b)*c^3/(d^5*f^10))}}}