Question 492964
It can be simplified first
{{{ 8*2^z = 18*12^z }}}
Divide both sides by {{{2}}}
{{{ 4*2^z = 9*12^z }}}
{{{ (2^z) / (12^z) = 9/4 }}
{{{ (2/12)^z = 9/4 }}}
{{{ (1/6)^z = (3/2)^2 }}}
Take the natural log of both sides
{{{ z*ln(1/6) = 2*ln(3/2) }}}
{{{ z = 2*((ln(3/2)) / ln(1/6)) }}}
{{{ z = 2*(.405465 / -1.79176) }}}
{{{ z = -.452589 }}}
{{{ z = -.453 }}}
check answer:
{{{ 8*2^(-.453) = 8*.7305 }}}
{{{ 5.844 }}}
and
{{{ 18*12^(-.453) = 5.839 }}}
I think this is close enough