SOLUTION: 2 log base 3 9x= 8

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Question 149961: 2 log base 3 9x= 8
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Alog%283%2C%289x%29%29=8 Start with the given equation.


log%283%2C%28%289x%29%5E2%29%29=8 Rewrite the left side using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%283%2C%2881x%5E2%29%29=8 Square 9x to get 81x%5E2



3%5E8=81x%5E2 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x



3%5E8=3%5E4x%5E2 Rewrite 81 as 3%5E4


3%5E8%2F3%5E4=x%5E2 Divide both sides by 3%5E4.


3%5E%288-4%29=x%5E2 Divide the terms on the left side by subtracting the exponents.


3%5E%284%29=x%5E2 Subtract


81=x%5E2 Raise 3 to the 4th power to get 81


0%2B-sqrt%2881%29=x Take the square root of both sides.


x=9 or x=-9 Take the square root of 81 to get 9 or -9


Since you cannot take the log of negative number, this means that we must disregard the possible solution x=-9





So the only solution is x=9