SOLUTION: log(small)4(x+3) + log(small)4 (x-3)=2 the fours are small in the bottom corner so that's why i put small.

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Question 195711: log(small)4(x+3) + log(small)4 (x-3)=2 the fours are small in the bottom corner so that's why i put small.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%28x%2B3%29%29%2Blog%284%2C%28x-3%29%29=2 Start with the given equation.


log%284%2C%28%28x%2B3%29%28x-3%29%29%29=2 Combine the logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29


%28x%2B3%29%28x-3%29=4%5E2 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> x=b%5Ey


%28x%2B3%29%28x-3%29=16 Square 4 to get 16


x%5E2-9=16 FOIL


x%5E2=16%2B9 Add 9 to both sides.


x%5E2=25 Combine like terms.


x=%22%22%2B-sqrt%2825%29 Take the square root of both sides.


x=sqrt%2825%29 or x=-sqrt%2825%29 Break up the "plus/minus"


x=5 or x=-5 Take the square root of 25 to get 5



So the possible solutions are x=5 or x=-5



However since you cannot take the log of a negative number, this rules out x=-5 as a solution (since plugging this value in results in a negative argument)

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Answer:

So the only solution is x=5