Question 554086
{{{ a^x*b^x = c }}}
Suppose  I say {{{ d = a^x }}} and {{{ e = b^x }}}
Then I have {{{ d*e = c }}}.
It is true that {{{ log(( d*e )) = log(d) + log(e) }}}
Take the log of both sides of the original equation
{{{ log(( a^x*b^x )) = log(( c )) }}}
{{{ log(( a^x )) + log(( b^x )) = log(( c )) }}}
{{{ x*log(( a )) + x*log(( b )) = log(( c )) }}}
{{{ x*( log(a) + log(b) ) = log(( c )) }}}
{{{ x*( .5 + .3 ) = 16 }}}
{{{ x = 16 / .8 }}}
{{{ x = 20 }}}
Sorry, I did the whole thing.