Question 1111150
A compute manufacturer finds that when x millions of dollars are spent on research, the profit, P(x), in millions of dollars is given by P(x)=20+5log base 3 (x+3). How much should be spent on research to make a profit of 40 million dollars?
:
{{{20+5*log(3,(x+3))}}} = 40
{{{5*log(3,(x+3))}}} = 40 - 20
{{{5*log(3,(x+3))}}} = 20
{{{log(3,(x+3))}}} = {{{20/5}}}
{{{log(3,(x+3))}}} = 4
the exponent equiv of logs
x + 3 = {{{3^4}}}
x + 3 = 81
x = 81 - 3
x = 78 spent on research