SOLUTION: 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

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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?
Found 2 solutions by MathLover1, ankor@dixie-net.com:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+P%28x%29=20%2B5log+%283%2Cx%2B3%29
if P%28x%29=+40(million dollars)
40+=20%2B5log+%283%2Cx%2B3%29
5log+%283%2Cx%2B3%29=40+-20
5log+%283%2Cx%2B3%29=20
log+%283%2Cx%2B3%29=20%2F5
log+%283%2Cx%2B3%29=4
log+%28x%2B3%29%2Flog%283%29=74
log+%28x%2B3%29=4%2Alog%283%29
log+%28x%2B3%29=log%283%5E4%29
x%2B3=3%5E4
x=81-3
x=78 millions

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B5%2Alog%283%2C%28x%2B3%29%29 = 40
5%2Alog%283%2C%28x%2B3%29%29 = 40 - 20
5%2Alog%283%2C%28x%2B3%29%29 = 20
log%283%2C%28x%2B3%29%29 = 20%2F5
log%283%2C%28x%2B3%29%29 = 4
the exponent equiv of logs
x + 3 = 3%5E4
x + 3 = 81
x = 81 - 3
x = 78 spent on research