Jamie won $50 in a raffle. Her brother Zack wants her to share her prize with him. She tells him that he can have the fractional part of her prize that is equal to the solution to the equation (2x+9)^5x-2=1 if he can solve the question. If Zack solves the equation correctly, how much will he receive?
-
Hi, should the 5x-2 part be in parentheses? i.e. (2x+9)^(5x-2)=1? In which case you can solve by taking the log of both sides:
Let a=(2x+9)
Let b=(5x-2)
log(a^b)=log(1)
b.log(a)=0
Solving for x gives x=-4 or 2/5, so Zak receives 2/5 of $50 = $20
Let a=(2x+9)
Let b=(5x-2)
log(a^b)=log(1)
b.log(a)=0
Solving for x gives x=-4 or 2/5, so Zak receives 2/5 of $50 = $20