SOLUTION: log(base5) x - log(base5)(x-2)= log(base5) 4 Many thanks.

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Question 165216This question is from textbook
: log(base5) x - log(base5)(x-2)= log(base5) 4
Many thanks. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%2C%28x%29%29-log%285%2C%28x-2%29%29=log%285%2C%284%29%29 Start with the given equation


log%285%2C%28%28x%29%2F%28x-2%29%29%29=log%285%2C%284%29%29 Combine the logs on the left side using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


%28x%29%2F%28x-2%29=4 Since the bases of the logs on both sides are equal, this means that the arguments of the logs (the stuff inside the logs) are equal


x=4%28x-2%29 Multiply both sides by x-2


x=4x-8 Distribute.


x-4x=-8 Subtract 4x from both sides.


-3x=-8 Combine like terms on the left side.


x=%28-8%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=8%2F3 Reduce.


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Answer:

So the answer is x=8%2F3 which approximates to x=2.667.